Latest build deployed.

.mapping.json

@@ -1 +1 @@
-{"source/main.ptx": ["my-great-book"], "source/frontmatter.ptx": ["frontmatter", "front-colophon"], "source/ch-Introduction.ptx": ["ch-Introduction", "sec-Introduction"], "source/ch-Probability.ptx": ["ch-Probability"], "source/sec-Set-Theory.ptx": ["sec-Set-Theory"], "source/sec-Probability.ptx": ["sec-Probability"], "source/sec-Conditional-Probability.ptx": ["sec-Conditional-Probability"], "source/sec-Independent-Events.ptx": ["sec-Independent-Events"], "source/ch-Random-Variables.ptx": ["ch-Random-Variables"], "source/sec-Discrete-RVs.ptx": ["sec-Discrete-RVs"], "source/sec-Continuous-RVs.ptx": ["sec-Continuous-RVs"], "source/sec-Joint-Distributions.ptx": ["sec-Joint-Distributions"], "source/ch-Expected-Value.ptx": ["ch-Expected-Value"], "source/sec-Expected-Value.ptx": ["sec-Expected-Value"], "source/sec-Variance.ptx": ["sec-Variance"], "source/sec-Covariance.ptx": ["sec-Covariance"], "source/ch-Confidence-Intervals.ptx": ["ch-Confidence-Intervals", "sec-CLT", "sec-Confidence-Intervals"], "source/ch-Hypothesis-Testing.ptx": ["ch-Hypothesis-Testing", "sec-One-Sample-Tests", "sec-Two-Sample-Tests", "sec-Power", "sec-Chi-Squared"], "source/ch-Linear-Regression.ptx": ["ch-Linear-Regression", "sec-Correlation", "sec-Linear-Regression"], "source/backmatter.ptx": ["backmatter"]}
+{"source/main.ptx": ["my-great-book", "frontmatter", "front-colophon", "ch-Introduction", "sec-Introduction", "ch-Probability", "sec-Set-Theory", "sec-Probability", "sec-Conditional-Probability", "sec-Independent-Events", "ch-Random-Variables", "sec-Discrete-RVs", "sec-Continuous-RVs", "sec-Joint-Distributions", "ch-Expected-Value", "sec-Expected-Value", "sec-Variance", "sec-Covariance", "ch-Confidence-Intervals", "sec-Likelihood", "sec-CLT", "sec-Confidence-Intervals", "ch-Hypothesis-Testing", "sec-One-Sample-Tests", "sec-Two-Sample-Tests", "sec-Power", "sec-Chi-Squared", "ch-Linear-Regression", "sec-Correlation", "sec-Linear-Regression", "backmatter"]}

_static/39.47c68f7dc05f7c3e.js.LICENSE.txt

@@ -0,0 +1,5 @@
+/*! Hammer.JS - v2.0.8 - 2016-04-23
+ * http://hammerjs.github.io/
+ *
+ * Copyright (c) 2016 Jorik Tangelder;
+ * Licensed under the MIT license */

_static/420.930dc253cc191e9e.js.LICENSE.txt

@@ -0,0 +1,5 @@
+/*! Hammer.JS - v2.0.8 - 2016-04-23
+ * http://hammerjs.github.io/
+ *
+ * Copyright (c) 2016 Jorik Tangelder;
+ * Licensed under the MIT license */

_static/_runestone-services.xml

@@ -1,7 +1,7 @@
 <?xml version="1.0" ?>
 <all>
 	<js type="list">
-		<item type="str">prefix-runtime.fc0e080e84d54281.bundle.js</item>
+		<item type="str">prefix-runtime.0d5f811896ddeac1.bundle.js</item>
 		<item type="str">prefix-723.3e6434f80549315a.bundle.js</item>
 		<item type="str">prefix-runestone.e2abc79debce15fd.bundle.js</item>
 	</js>
@@ -10,5 +10,5 @@
 		<item type="str">prefix-runestone.6ec5960970d8b364.css</item>
 	</css>
 	<cdn-url type="str">https://runestone.academy/cdn/runestone/</cdn-url>
-	<version type="str">7.11.11</version>
+	<version type="str">7.11.13</version>
 </all>

_static/pretext/js/knowl.js

@@ -0,0 +1,338 @@
+// Code controlling behavior of xref knowls and born hidden knowls
+
+// Assumes this file is loaded as part of initial page
+window.addEventListener("load", (event) => {
+  addKnowls(document);
+});
+
+function addKnowls(target) {
+  const xrefs = target.querySelectorAll("[data-knowl]");
+  for (const xref of xrefs) {
+    LinkKnowl.initializeXrefKnowl(xref);
+  }
+
+  const bornHiddens = target.querySelectorAll(".born-hidden-knowl");
+  for (const bhk of bornHiddens) {
+    const summary = bhk.querySelector(":scope > summary");
+    const contents = bhk.querySelector(":scope > summary + *");
+    new SlideRevealer(summary, contents, bhk);
+  }
+}
+
+// Used to animate both types of knowls
+class SlideRevealer {
+  static STATE = Object.freeze({
+    INACTIVE: 0,
+    CLOSING: 1,
+    EXPANDING: 2
+  });
+
+  // triggerElement is the element clicked to open/close
+  // contentElement is the element that will hide/reveal
+  // animatedElement is the element that will grow/shrink as contentElement is modified
+  //    may be the same as contentElement or a parent of it
+  constructor(triggerElement, contentElement, animatedElement) {
+    this.triggerElement = triggerElement;
+    this.contentElement = contentElement;
+    this.animatedElement = animatedElement;
+
+    // mid animation state tracking
+    this.animation = null;
+    this.animationState = SlideRevealer.STATE.INACTIVE;
+
+    this.triggerElement.addEventListener('click', (e) => this.onClick(e));
+  }
+
+  onClick(e) {
+    // Stop default behavior from the browser
+    if (e) e.preventDefault();
+
+    // Add an overflow on the <details> to avoid content overflowing
+    this.animatedElement.style.overflow = 'hidden';
+
+    // Check if the element is being closed or is already closed
+    if (this.animationState === SlideRevealer.STATE.CLOSING || !this.animatedElement.hasAttribute("open")) {
+      // Force the [open] attributes - allow for similar targetting of xref and born-hidden knowls
+      this.animatedElement.setAttribute("open","");
+      this.triggerElement.setAttribute("open","");
+      this.contentElement.style.display = '';
+      // Trigger the animation to expand or collapse the knowl.
+      // Delay the MathJax typesetting until the knowl is visible to ensure proper measurements
+      // are taken, but before the unrolling begins. This helps avoid layout shifts and ensures
+      // smooth animation with correctly sized content.
+      MathJax.typesetPromise().then(() => window.requestAnimationFrame(() => this.toggle(true)));
+    } else if (this.animationState === SlideRevealer.STATE.EXPANDING || this.animatedElement.hasAttribute("open")) {
+      this.toggle(false);
+    }
+  }
+
+  toggle(expanding) {
+    let closedHeight = 0;
+    if (this.animatedElement.contains(this.triggerElement))
+      closedHeight = this.triggerElement.offsetHeight;
+    const fullHeight = closedHeight + this.contentElement.offsetHeight;
+
+    const startHeight = `${expanding ? closedHeight : fullHeight}px`;
+    const endHeight = `${expanding ? fullHeight : closedHeight}px`;
+
+    // Need to animate padding to avoid extra height for xref knowls
+    const padding = this.animatedElement.offsetHeight - this.animatedElement.clientHeight;
+    const startPad = `${expanding ? 0 : padding}px`;
+    const endPad = `${expanding ? padding : 0}px`;
+
+    // Cancel any existing animation
+    if (this.animation) {
+      this.animation.cancel();
+    }
+
+    // Animate ~400 pixels per second with max of 0.75 second and min of 0.25
+    const animDuration = Math.max( Math.min( (Math.abs(closedHeight - fullHeight) / 400 * 1000), 750), 250);
+
+    // Start animation
+    this.animationState = expanding ? SlideRevealer.STATE.EXPANDING : SlideRevealer.STATE.CLOSING;
+    this.animation = this.animatedElement.animate({
+      height: [startHeight, endHeight],
+      paddingTop: [startPad, endPad],
+      paddingBottom: [startPad, endPad]
+    }, {
+      duration: animDuration,
+      easing: 'ease'
+    });
+
+    this.animation.onfinish = () => { this.onAnimationFinish(expanding); };
+    this.animation.oncancel = () => { this.animationState = SlideRevealer.STATE.INACTIVE; };
+  }
+
+  onAnimationFinish(isOpen) {
+    // Clear animation state
+    this.animation = null;
+    this.animationState = SlideRevealer.STATE.INACTIVE;
+
+    // Make sure animated element has open (needed for details)
+    if(!isOpen) {
+      this.animatedElement.removeAttribute("open");
+      this.triggerElement.removeAttribute("open");
+    }
+
+    // Clear styles used in animation
+    this.animatedElement.style.overflow = '';
+    if (!isOpen)
+      this.contentElement.style.display = 'none';
+
+    if (isOpen) {
+      let hasCallback = this.contentElement.querySelectorAll("[data-knowl-callback]");
+      hasCallback.forEach((el) => {
+        window[el.getAttribute("data-knowl-callback")](el, open);
+      });
+    }
+  }
+}
+
+
+
+// A LinkKnowl manages a single link based knowl
+class LinkKnowl {
+  // Used to uniquely identify XrefKnowls
+  static xrefCount = 0;
+
+  // Factory to create an XrefKnowl from a knowl link
+  // Will avoid duplicate initialization
+  // This should be used by outside code to create XrefKnowls
+  static initializeXrefKnowl(knowlLinkElement) {
+    if (knowlLinkElement.getAttribute("data-knowl-uid") === null) {
+      return new LinkKnowl(knowlLinkElement);
+    }
+  }
+
+  // "Private" constructor - should only be called by initializeXrefKnowl
+  constructor(knowlLinkElement) {
+    this.linkElement = knowlLinkElement;
+    this.outputElement = null;
+    this.uid = LinkKnowl.xrefCount++;
+    knowlLinkElement.setAttribute("data-knowl-uid", this.uid);
+
+    // Xref's behavior is that of a button
+    knowlLinkElement.setAttribute("role", "button");
+
+    // Stash a copy of the original title for use in aria-label
+    // If no title, use textContent
+    knowlLinkElement.setAttribute("data-base-title", knowlLinkElement.getAttribute("title") || this.linkElement.textContent);
+
+    knowlLinkElement.classList.add("knowl__link");
+
+    this.updateLabels(false);
+
+    // Bind required to force "this" of event handler to be this object
+    knowlLinkElement.addEventListener("click", this.handleLinkClick.bind(this));
+  }
+
+  // Set aria-label and title based on visibility of knowl
+  updateLabels(isVisible) {
+    const verb = isVisible
+      ? this.linkElement.getAttribute("data-close-label") || "Close"
+      : this.linkElement.getAttribute("data-reveal-label") || "Reveal";
+    const targetDescript = this.linkElement.getAttribute("data-base-title");
+    const helpText = verb + " " + targetDescript;
+
+    this.linkElement.setAttribute("aria-label", helpText);
+    this.linkElement.setAttribute("title", helpText);
+  }
+
+  // Toggle the state of the knowl link and output elements
+  // Assumes output is already created
+  toggle() {
+    this.linkElement.classList.toggle("active");
+    const isActive = this.linkElement.classList.contains("active");
+    this.updateLabels(isActive);
+
+    // Scroll to reveal if needed
+    if (isActive) {
+      const h = this.outputElement.getBoundingClientRect().height;
+      if (h > window.innerHeight) {
+        // knowl is taller than window, scroll to top of knowl
+        this.outputElement.scrollIntoView(true);
+      } else {
+        // reveal full knowl
+        if (this.outputElement.getBoundingClientRect().bottom > window.innerHeight)
+          this.outputElement.scrollIntoView(false);
+      }
+    }
+  }
+
+  // Returns element the knowl output should be inserted after
+  findOutputLocation() {
+    const invalidParents = "table, mjx-container, div.tabular-box, .runestone > .parsons";
+    // Start with the link's parent, move up as long as there are invalid parents
+    let el = this.linkElement.parentElement;
+    let problemAncestor = el.closest(invalidParents);
+    while (problemAncestor && problemAncestor !== el) {
+      el = problemAncestor;
+      problemAncestor = el.closest(invalidParents);
+    }
+    return el;
+  }
+
+  // Create the knowl output element
+  createOutputElement() {
+    const outputId = "knowl-uid-" + this.uid;
+    const outputContentsId = "knowl-output-" + this.uid;
+    const linkTarget = this.linkElement.getAttribute("data-knowl");
+
+    const placeholderText = `<div class='knowl__content' style='display:none;' id='${outputId}' aria-live='polite' id='${outputContentsId}'>`
+      + `Loading '${linkTarget}'`
+      + `</div>`;
+
+    const temp = document.createElement("template");
+    temp.innerHTML = placeholderText;
+    this.outputElement = temp.content.children[0];
+
+    const insertLoc = this.findOutputLocation(this.linkElement);
+    insertLoc.after(this.outputElement);
+  }
+
+  // Get content for knowl as dom element. Returns promise that resolves to knowl content
+  async getContent() {
+    const contentURL = this.linkElement.getAttribute("data-knowl");
+    const knowlContent = await fetch(contentURL)
+      .then((response) => response.text())
+      .then((data) => {
+        // knowls are full HTML pages, need to just extract body
+        let knowlDoc = (new DOMParser()).parseFromString(data, "text/html");
+        let tempContainer = knowlDoc.body;
+        // grab any scripts from head of knowl doc and add them to the output
+        let scripts = knowlDoc.querySelectorAll("head script");
+        tempContainer.append(...scripts);
+        return tempContainer;
+      })
+      .catch((error) => {
+        const destination = this.linkElement.getAttribute("href");
+        const text = this.linkElement.textContent;
+        const err_message = `<div class='knowl-output__error'>`
+          + `<div class='para'>Error fetching content. (<em>${error}</em>)</div>`
+          + `<div class='para'><a href='${destination}'>Navigate to ${text}</a> instead.</div>`
+          + `<div class='para'>If you are viewing this book from your local filesystem, this is expected behavior. To view the book with all features, you must serve the book from a web server. See the <a href="https://pretextbook.org/doc/guide/html/author-faq.html#how-do-i-view-my-book-locally">PreTeXt FAQ</a> for more information.</div>`
+          + `</div>`;
+        return err_message;
+      });
+    return knowlContent;
+  }
+
+  // Handle a click on the knowl link
+  handleLinkClick(event) {
+    // prevent navigation
+    event.preventDefault();
+
+    if (this.outputElement !== null) {
+      // output already created, toggle visibility
+      this.toggle();
+    } else {
+      this.createOutputElement();
+
+      const slideHandler = new SlideRevealer(this.linkElement, this.outputElement, this.outputElement);
+      //slideHandler is now responsible for handling clicks to this element
+      this.linkElement.addEventListener('click', slideHandler);
+
+      // Wait up to a half second in hopes of avoiding double content change
+      // then render to show loading message
+      let loadingTimeout = setTimeout(() => {
+        loadingTimeout = null;
+        slideHandler.onClick(); //fake initial click
+        this.toggle();
+      }, 500);
+
+      const content = this.getContent();
+
+      // Content is a promise at this point, insert when resolved
+      content
+        .then((tempContainer) => {
+          // if timeout still active, cancel it and render
+          if (loadingTimeout !== null) {
+            clearTimeout(loadingTimeout);
+          }
+          // Now give code that follows .1 seconds to render before making visible
+          setTimeout(() => {
+            slideHandler.onClick(); //fake initial click
+            this.toggle();
+          }, 100);
+
+          // check embedded runestone interactives by loading content into a temp container
+          // we want to not render any that already are on page. Dupe IDs probably bad
+          const runestoneElements = tempContainer.querySelectorAll(".ptx-runestone-container");
+          [...runestoneElements].forEach((e) => {
+            const rsId = e.querySelector("[data-component]")?.id;
+            const onPage = document.getElementById(rsId);
+            if (onPage) {
+              e.innerHTML = `<div class="para">The interactive that belongs here is already on the page and cannot appear multiple times. <a href="#${rsId}">Scroll to interactive.</a>`;
+            } else {
+              // let runestone start rendering it
+              window.runestoneComponents.renderOneComponent(e);
+            }
+          });
+
+          // now move all contents to the real output element
+          const children = [...tempContainer.children];
+          this.outputElement.innerHTML = "";
+          this.outputElement.append(...children);
+
+          // render any knowls and mathjax in the knowl
+          addKnowls(this.outputElement);
+
+          // try prism highlighting
+          Prism.highlightAllUnder(this.outputElement);
+
+          // force any scripts (e.g. sagecell) to execute by evaling them
+          [...this.outputElement.getElementsByTagName("script")].forEach((s) => {
+            if (
+              s.getAttribute("type") === null ||
+              s.getAttribute("type") === "text/javascript"
+            ) {
+              eval(s.innerHTML);
+            }
+          });
+        })
+        .catch((data) => {
+          console.log("Error fetching knowl content: " + data);
+        });
+    }
+  }
+}

_static/pretext/js/mathjaxknowl3.js

@@ -0,0 +1,48 @@
+
+      const { Configuration } = MathJax._.input.tex.Configuration;
+      const { CommandMap } = MathJax._.input.tex.SymbolMap;
+      const NodeUtil = MathJax._.input.tex.NodeUtil.default;
+
+      var GetArgumentMML = function (parser, name) {
+        var arg = parser.ParseArg(name);
+        if (!NodeUtil.isInferred(arg)) {
+          return arg;
+        }
+        var children = NodeUtil.getChildren(arg);
+        if (children.length === 1) {
+          return children[0];
+        }
+        var mrow = parser.create("node", "mrow");
+        NodeUtil.copyChildren(arg, mrow);
+        NodeUtil.copyAttributes(arg, mrow);
+        return mrow;
+      };
+
+      let mathjaxKnowl = {};
+      /**
+       * Implements \knowl{url}{math}
+       * @param {TexParser} parser The calling parser.
+       * @param {string} name The TeX string
+       */
+      mathjaxKnowl.Knowl = function (parser, name) {
+        var url = parser.GetArgument(name);
+        var arg = GetArgumentMML(parser, name);
+        var mrow = parser.create("node", "mrow", [arg], {
+            tabindex: '0',
+            "data-knowl": url
+        });
+        parser.Push(mrow);
+      };
+
+      new CommandMap(
+        "knowl",
+        {
+          knowl: ["Knowl"]
+        },
+        mathjaxKnowl
+      );
+      const configuration = Configuration.create("knowl", {
+        handler: {
+          macro: ["knowl"]
+        }
+      });

_static/pretext/js/pretext-stack/stackapicalls.js

@@ -17,6 +17,14 @@ const stackstring = {
   "api_correct":"Correct answers"
 };
 
+
+function wrap_math(content) {
+  // Wrap instances of \[ ... \] and \( ... \) into the tags configured to be processed by MathJax
+  // Here we make sure that the backslashes are not escaped like \\[ 
+  content = content.replace(/(?<!\\)(\\\(.*?(?<!\\)\\\))/g, "<span class=\"process-math\">$1</span>");
+  return content.replace(/(?<!\\)(\\\[.*?(?<!\\)\\\])/g, "<span class=\"process-math\">$1</span>");
+}
+
 // Create data for call to API.
 async function collectData(qfile, qname, qprefix) {
   let res = "";
@@ -95,6 +103,7 @@ function send(qfile, qname, qprefix) {
           // This is a bit of a hack. The question render returns an <a href="..."> calling the download function with
           // two arguments. We add the additional arguments that we need for context (question definition) here.
           question = question.replace(/javascript:download\(([^,]+?),([^,]+?)\)/, `javascript:download($1,$2, '${qfile}', '${qname}', '${qprefix}', ${seed})`);
+          question = wrap_math(question);
           if (input.samplesolutionrender && name !== 'remember') {
             // Display render of answer and matching user input to produce the answer.
             correctAnswers += `<p>
@@ -102,7 +111,7 @@ function send(qfile, qname, qprefix) {
                   ${stackstring['api_which_typed']}: `;
             for (const [name, solution] of Object.entries(input.samplesolution)) {
               if (name.indexOf('_val') === -1) {
-                correctAnswers += `<span class='correct-answer'>${solution}</span>`;
+                correctAnswers += `<span class='correct-answer'>${wrap_math(solution)}</span>`;
               }
             }
             correctAnswers += '.</p>';
@@ -147,7 +156,7 @@ function send(qfile, qname, qprefix) {
         let sampleText = json.questionsamplesolutiontext;
         if (sampleText) {
           sampleText = replaceFeedbackTags(sampleText,qprefix);
-          document.getElementById(`${qprefix+'generalfeedback'}`).innerHTML = sampleText;
+          document.getElementById(`${qprefix+'generalfeedback'}`).innerHTML = wrap_math(sampleText);
           document.getElementById(`${qprefix+'stackapi_generalfeedback'}`).style.display = 'block';
         } else {
           // If the question is updated, there may no longer be general feedback.
@@ -165,7 +174,7 @@ function send(qfile, qname, qprefix) {
         document.getElementById(`${qprefix+'stackapi_correct'}`).style.display = 'none';
 
         createIframes(json.iframes);
-        MathJax.Hub.Queue(["Typeset", MathJax.Hub]);
+        MathJax.typeset();
       }
       catch(e) {
         console.log(e);
@@ -207,14 +216,14 @@ function validate(element, qfile, qname, qprefix) {
         renameIframeHolders();
         const validationHTML = json.validation;
         const element = document.getElementsByName(`${qprefix+validationPrefix + answerName}`)[0];
-        element.innerHTML = validationHTML;
+        element.innerHTML = wrap_math(validationHTML);
         if (validationHTML) {
           element.classList.add('validation');
         } else {
           element.classList.remove('validation');
         }
         createIframes(json.iframes);
-        MathJax.Hub.Queue(["Typeset", MathJax.Hub]);
+        MathJax.typeset();
       }
       catch(e) {
         document.getElementById(`${qprefix+'errors'}`).innerText = http.responseText;
@@ -274,7 +283,7 @@ function answer(qfile, qname, qprefix, seed) {
             json.specificfeedback = json.specificfeedback.replace(name, getPlotUrl(file));
           }
           json.specificfeedback = replaceFeedbackTags(json.specificfeedback,qprefix);
-          specificFeedbackElement.innerHTML = json.specificfeedback;
+          specificFeedbackElement.innerHTML = wrap_math(json.specificfeedback);
           specificFeedbackElement.classList.add('feedback');
         } else {
           specificFeedbackElement.classList.remove('feedback');
@@ -292,7 +301,7 @@ function answer(qfile, qname, qprefix, seed) {
                     ${(json.scores[name] * json.scoreweights[name] * json.scoreweights.total).toFixed(2)}
                       / ${(json.scoreweights[name] * json.scoreweights.total).toFixed(2)}.</div>`;
             }
-            element.innerHTML = fb;
+            element.innerHTML = wrap_math(fb);
             // if (fb) {
 //                   element.classList.add('feedback');
 //                 } else {
@@ -301,7 +310,7 @@ function answer(qfile, qname, qprefix, seed) {
           }
         }
         createIframes(json.iframes);
-        MathJax.Hub.Queue(["Typeset", MathJax.Hub]);
+        MathJax.typeset();
       }
       catch(e) {
         console.log(e);

_static/pretext/js/pretext.js

@@ -133,25 +133,6 @@ window.addEventListener("DOMContentLoaded",function(event) {
     }
 });
 
-/* jump to next page if reader tries to scroll past the bottom */
-// var hitbottom = false;
-// window.onscroll = function(ev) {
-//   if ((window.innerHeight + window.scrollY) >= document.body.scrollHeight) {
-//     // you're at the bottom of the page
-//     console.log("Bottom of page");
-//     if (hitbottom) {
-//         console.log("hit bottom again");
-//         thenextbutton = document.getElementsByClassName("next-button")[0];
-//         thenextbutton.click();
-//     } else {
-//         hitbottom = true;
-//         /* only jump to next page if hard scroll in quick succession */
-//         window.scrollBy(0, -20);
-//         setTimeout(function (){ hitbottom = false }, 1000);
-//     }
-//   }
-// };
-
 
 //-----------------------------------------------------------------------------
 // Dynamic TOC logic
@@ -246,7 +227,30 @@ window.addEventListener("DOMContentLoaded", function(event) {
                 expander.title = "Expand" + (itemType !== "" ? " " + itemType : "");
             }
         }
-      }
+    }
+
+    //Do we have a hash in the URL? If so, we need to identify up to make sure
+    // all parents of that item are expanded
+    if(window.location.hash) {
+        let hash = window.location.hash;
+        // find the link in the TOC that has an href ending in this hash
+        let hashLink = document.querySelector(`.ptx-toc a[href$="${hash}"]`);
+        if(hashLink) {
+            let parentTocItem = hashLink.closest(".toc-item");
+            while(parentTocItem && !parentTocItem.classList.contains("contains-active")) {
+                parentTocItem.classList.add("contains-active");
+                let expander = parentTocItem.querySelector(".toc-expander");
+                if(expander) {
+                    //make sure it is expanded
+                    if(!parentTocItem.classList.contains("expanded")) {
+                        toggleTOCItem(expander);
+                    }
+                }
+                parentTocItem = parentTocItem.parentElement.closest(".toc-item");
+            }
+        }
+    }
+
 });
 
 // This needs to be after the TOC's geometry is settled

_static/pretext/js/pretext_add_on.js

@@ -15,13 +15,6 @@
 console.log("thisbrowser.userAgent", window.navigator.userAgent);
 */
 
-var minivers = "0";
-if (typeof miniversion !== 'undefined') {
-  console.log("typeof miniversion", typeof miniversion, "dddd", typeof miniversion == 'undefined');
-  minivers = miniversion.toString();
-}
-console.log("               minivers", minivers);
-
 /* scrollbar width from https://stackoverflow.com/questions/13382516/getting-scroll-bar-width-using-javascript */
 function getScrollbarWidth() {
     var outer = document.createElement("div");
@@ -289,22 +282,8 @@ function updateURLParameter(url, param, paramVal){
   return baseURL + "?" + newAdditionalURL + rows_txt;
 }
 
-function WWiframeReseed(iframe, seed) {
-  var this_problem = document.getElementsByName(iframe)[0];
-  var this_problem_url = this_problem.src;
-  if (seed === undefined){seed = Number(this_problem.getAttribute('data-seed')) + 80 + 84 + 88;}
-  this_problem.setAttribute('data-seed', seed);
-  this_problem_url = updateURLParameter(this_problem_url, "problemSeed", seed);
-  this_problem.src = this_problem_url;
-}
-
 function process_workspace() {
     console.log("processing workspace");
-// next does not work, because the cursor does back to the beginning
-// so:  need to handle the cursor
-//    the_text = document.activeElement.innerHTML;
-//    the_text = the_text.replace(/(^|\s)\$([^\$]+)\$(\s|$|[.,!?;:])/g, "\1\\(\2\\)\3")
-//    document.activeElement.innerHTML = the_text
     MathJax.typesetPromise();
 }
 /* for the GeoGebra calculator */
@@ -352,17 +331,8 @@ window.addEventListener("load",function(event) {
                  ggbscript.id = "create_ggb_calc";
                  ggbscript.innerHTML = "ggbApp.inject('geogebra-calculator')";
                  document.body.appendChild(ggbscript);
-//                 setTimeout( function() {
-//                     $("#calculator-toggle").focus();
-//                     var inputfield = $("input.gwt-SuggestBox.TextField")[0];
-//                     console.log("inputfield", inputfield);
-//                     inputfield.focus();
-//                 }, 4000);
              } else {
                  pretext_geogebra_calculator_onload();
-//                 var inputfield = $("input.gwt-SuggestBox.TextField")[0];
-//                 console.log("inputfield", inputfield);
-//                 inputfield.focus();
              }
          } else {
              $('#calculator-container').css('display', 'none');
@@ -374,16 +344,6 @@ window.addEventListener("load",function(event) {
 });
 
 
-/*
-window.addEventListener("load",function(event) {
-//    setTimeout( function() {
-       console.log("changein play color");
-       $('figure > div.onclick > svg > path').attr('fill', '#0000aa');
-       $('path').attr('fill', '#0000aa')
-//    }, 5000)
-});
-*/
-
 window.addEventListener("load",function(event) {
     document.onkeyup = function(event)
     {
@@ -402,14 +362,6 @@ window.addEventListener("load",function(event) {
                     console.log("staying in the sage cell", parent_sage_cell, document.activeElement)
                     just_hit_escape = true;
                     setTimeout(function(){ just_hit_escape = false }, 1000);
-     //           console.log("parent_sage_cell", parent_sage_cell);
-     //           if ($(parent_sage_cell).hasClass('sagecell_editor')) {
-     //              console.log("I am trapped in a sage cell", $(document.activeElement).closest(".sagecell_editor"));
-     //              console.log($(document.activeElement));
-     //              var this_sage_cell = $(document.activeElement).closest(".sagecell_editor");
-     //              this_sage_cell.next().focus;
-     //           }
-     //           else
                 } else
                 if(knowl_focus_stack.length > 0 ) {
                    most_recently_opened = knowl_focus_stack.pop();
@@ -426,144 +378,6 @@ window.addEventListener("load",function(event) {
 },
 false);
 
-// a hack for hosted tracking
-
-window.addEventListener("load",function(event) {
-       if($('body').attr('id') == "judson-AATA") {
-           console.log("            found AATA");
-           console.log(" looking for id");
-           if (typeof eBookConfig !== 'undefined') {
-             if(eBookConfig['username']) {
-                aa_id = "run" + eBookConfig['username'];
-                ut_id = eBookConfig['username'];
-             console.log(" done looking for id", ut_id);
-var newscript = document.createElement('script');
-  newscript.type = 'text/javascript';
-  newscript.async = true;
-  newscript.src = 'https://pretextbook.org/js/' + '0.13' + '/' + 'trails' + '.js';
-  var allscripts = document.getElementsByTagName('script');
-  var s = allscripts[allscripts.length - 1];
-  console.log('s',s);
-  console.log("adding a script", newscript);
-  s.parentNode.insertBefore(newscript, s.nextSibling);
-  trail = true;
-             console.log(" done adding script");
-             } else {
-             console.log(" did not find username");
-             }
-           }  else {
-             console.log(" did not find eBookConfig")
-           }
-       }
-});
-
-function loadResource(type, file) {
-  /* type should be js or css */
-  if (typeof js_version === 'undefined') { js_version = '0.2' }
-  if (typeof css_version === 'undefined') { css_version = '0.6' }
-  var newresource, allresources, s;
-  var linktype = "script";
-  if (type == "css") { linktype = "link" }
-  newresource = document.createElement(linktype);
-
-  if (type == "css") {
-      newresource.type = 'text/css';
-      newresource.rel = 'stylesheet';
-      newresource.href = 'https://pretextbook.org/css/' + css_version + '/' + file + '.css';
-      newresource.href += '?minivers=' + minivers;
-  } else if (type == "js") {
-      newresource.type = 'text/javascript';
-//  newscript.async = true;
-      newresource.src = 'https://pretextbook.org/js/' + js_version + '/' + file + '.js';
-      newresource.src += '?minivers=' + minivers;
-  } else {
-      console.log("unknown resource type", type, "for", file);
-      return
-  }
-
-  allresources = document.getElementsByTagName(linktype);
-  s = allresources[allresources.length - 1];
-  console.log('s',s);
-  console.log("adding a resource", newresource);
-  s.parentNode.insertBefore(newresource, s.nextSibling);
-}
-
-
-window.addEventListener("load",function(event) {
-       if(false && $('body').attr('id') == "pretext-SA") {
-           console.log("            found DMOI");
-           if (typeof uname === "undefined") { uname = "" }
-           console.log("aaaa", uname, "  uname");
-           if(uname == "editor") {
-                loadResource('js', 'edit');
-           } else {
-                console.log("not enabling editing")
-           }
- /*       } else if ($('body').attr('id') == "pugetsound-SW") { */
-        } else if (false && window.location.href.includes("soundwriting.pugetsound")) {
-/* a bunch of temporary exploration for a Sound Writing survey */
-            console.log("please take our survey");
-            console.log(window.location.href);
-            console.log(window.location.href.includes("soundwriting.pugetsound"));
-
-            loadResource("js", "login");
-            loadResource("css", "features");
-            setTimeout( loadResource("js", "survey"), 1000);  /* I know: sloppy */
-
-  //      } else if ((typeof online_editable !== 'undefined') &&  online_editable) {
-        } else if (false && $('body').attr('id') == "pretext-SA") {
-            loadResource('css', 'features');
-            loadResource('js', 'login')
-            loadResource('js', 'edit');
-        } else {
-            var this_source_txt;
-            var source_url = window.location.href;
-            source_url = source_url.replace(/(#|\?).*/, "");
-            source_url = source_url.replace(/html$/, "ptx");
-            if (typeof sourceeditable !== 'undefined') {
-              fetch(source_url).then(
-                  function(u){ return u.text();}
-                ).then(
-                  function(text){
-                      this_source_txt = text;
-                      if (this_source_txt.includes("404 Not")) {
-                          console.log("Editing not enabled: source unavailable")
-                      } else {
-                        loadResource('css', 'features');
-                        loadResource('css', 'edit');
-                        loadResource('js', 'login')
-                        loadResource('js', 'edit');
-                      }
-                  }
-                );
-              } else {
-                   console.log("Source file unavailable: editing not possible")
-              }
-        }
-
-});
-
-// this is to open every knowl on a page
-// (this code is not actually used anywhere)
-window.addEventListener("load",function(event) {
-   if($('body').hasClass("braillesample")) {
-       var knowl_id_counterX = 0;
-       console.log("            found braillesample");
-       var all_knowls = $('[data-knowl]');
-       console.log("found", all_knowls.length, "knowls");
-       console.log("which are", all_knowls);
-       for (var j=1; j < all_knowls.length; ++j) {
-           console.log(j, "un-knowling", all_knowls[j]);
-           console.log("attr", $(all_knowls[j]).attr("data-knowl"));
-           $knowl = $(all_knowls[j]);
-           if(!$knowl.attr("data-knowl-uid")) {
-              $knowl.attr("data-knowl-uid", knowl_id_counterX);
-              knowl_id_counterX++;
-            }
-            knowl_click_handler($knowl);
-          // knowl_click_handler($(all_knowls[j]))
-       }
-}});
 
 // when the anchor is a knowl, open it
 window.addEventListener("load",function(event) {
@@ -594,13 +408,6 @@ window.addEventListener("load",function(event) {
 });
 
 
-// What purpose does this serve?
-function urlattribute() {
-        var this_urlstub = window.location.hostname;
-        document.body.setAttribute("data-urlstub", this_urlstub);
-}
-
-
 // The new method for creating pages and adjusting workspace //
 
 // This is used multiple places to set height of workspace divs to their author-provided heights
@@ -614,6 +421,7 @@ function setInitialWorkspaceHeights() {
 
 // If a printout (worksheet or handout) includes authored pages, we only need to put content before the first page and after the last page into the first and last pages, respectively.
 function adjustPrintoutPages() {
+    console.log("*** Adjusting printout pages.");
     const printout = document.querySelector('section.worksheet, section.handout');
     if (!printout) {
         console.warn("No printout found, exiting adjustPrintoutPages.");
@@ -647,6 +455,7 @@ function adjustPrintoutPages() {
 
 // This is the main function we will call then a printout does not come from the XSL with pages already defined (for now, the XSL will keep the <page> behavior as an option).
 function createPrintoutPages(margins) {
+    console.log("*** Creating printout pages with margins:", margins);
 
     // Assumptions: needs to work for both letter (8.5in x 11in) and a4 (210mm x 297mm) paper sizes.  We will work in pixels (96/in): those are 816px x 1056px and 794px x 1122.5px respectively (1 inch = 96 px, 1 cm = 37.8 px).  We assume that the printing interface of the browser will do the right thing with these.
 
@@ -679,16 +488,6 @@ function createPrintoutPages(margins) {
                 printout.insertBefore(tasks[i], child.nextSibling);
             }
         // Skipping separate treatment of exercisegroups for now.
-        //} else if (child.classList.contains('exercisegroup')) {
-        //    for (const subChild of child.children) {
-        //        if (subChild.classList.contains('exercisegroup-exercises')){
-        //            for (const row of subChild.children){
-        //                rows.push(row);
-        //            }
-        //        } else {
-        //            rows.push(child);
-        //        }
-        //    }
         } else {
             rows.push(child);
         }
@@ -743,10 +542,90 @@ function createPrintoutPages(margins) {
     }
 }
 
+// Add headers and footers to all pages in a printout.  Start with this set to be hidden by default; a toggle later will show/hide them.
+function addHeadersAndFootersToPrintout() {
+    const printout = document.querySelector('section.worksheet, section.handout');
+    if (!printout) {
+        console.warn("No printout found, exiting addHeadersAndFootersToPrintout.");
+        return;
+    }
+    const pages = printout.querySelectorAll('.onepage');
+    // Loop through pages and add header and footer divs
+    pages.forEach((page, index) => {
+        const isFirstPage = index === 0;
+        // Add header
+        const headerDiv = document.createElement('div');
+        headerDiv.classList.add(isFirstPage ? 'first-page-header' : 'running-header', 'hidden');
+        headerDiv.innerHTML = `<div class="header-left" contenteditable="true"></div><div class="header-center" contenteditable="true"></div><div class="header-right" contenteditable="true"></div>`;
+        page.insertBefore(headerDiv, page.firstChild);
+        // Add footer
+        const footerDiv = document.createElement('div');
+        footerDiv.classList.add(isFirstPage ? 'first-page-footer' : 'running-footer', 'hidden');
+        footerDiv.innerHTML = `<div class="footer-left" contenteditable="true"></div><div class="footer-center" contenteditable="true"></div><div class="footer-right" contenteditable="true"></div>`;
+        page.appendChild(footerDiv);
+    });
+    // Add content based on local storage if available, otherwise from data-attributes on the printout
+    const headerFooterKeys = ['header-first-left', 'header-first-center', 'header-first-right', 'footer-first-left', 'footer-first-center', 'footer-first-right', 'header-running-left', 'header-running-center', 'header-running-right', 'footer-running-left', 'footer-running-center', 'footer-running-right'];
+    const headerFooterContent = {};
+    headerFooterKeys.forEach(key => {
+        headerFooterContent[key] = localStorage.getItem(key) || printout.getAttribute(`data-${key}`) || '';
+    });
+    // First page header and footer
+    document.querySelector('.first-page-header').querySelector('.header-left').innerHTML = headerFooterContent['header-first-left'];
+    document.querySelector('.first-page-header').querySelector('.header-center').innerHTML = headerFooterContent['header-first-center'];
+    document.querySelector('.first-page-header').querySelector('.header-right').innerHTML = headerFooterContent['header-first-right'];
+    document.querySelector('.first-page-footer').querySelector('.footer-left').innerHTML = headerFooterContent['footer-first-left'];
+    document.querySelector('.first-page-footer').querySelector('.footer-center').innerHTML = headerFooterContent['footer-first-center'];
+    document.querySelector('.first-page-footer').querySelector('.footer-right').innerHTML = headerFooterContent['footer-first-right'];
+    // Running headers and footers
+    document.querySelectorAll('.running-header').forEach(headerDiv => {
+        headerDiv.querySelector('.header-left').innerHTML = headerFooterContent['header-running-left'];
+        headerDiv.querySelector('.header-center').innerHTML = headerFooterContent['header-running-center'];
+        headerDiv.querySelector('.header-right').innerHTML = headerFooterContent['header-running-right'];
+    });
+    document.querySelectorAll('.running-footer').forEach(footerDiv => {
+        footerDiv.querySelector('.footer-left').innerHTML = headerFooterContent['footer-running-left'];
+        footerDiv.querySelector('.footer-center').innerHTML = headerFooterContent['footer-running-center'];
+        footerDiv.querySelector('.footer-right').innerHTML = headerFooterContent['footer-running-right'];
+    });
+    // Add event listeners to update local storage when content is edited
+    headerFooterKeys.forEach(key => {
+        const selectorMap = {
+            'header-first-left': '.first-page-header .header-left',
+            'header-first-center': '.first-page-header .header-center',
+            'header-first-right': '.first-page-header .header-right',
+            'footer-first-left': '.first-page-footer .footer-left',
+            'footer-first-center': '.first-page-footer .footer-center',
+            'footer-first-right': '.first-page-footer .footer-right',
+            'header-running-left': '.running-header .header-left',
+            'header-running-center': '.running-header .header-center',
+            'header-running-right': '.running-header .header-right',
+            'footer-running-left': '.running-footer .footer-left',
+            'footer-running-center': '.running-footer .footer-center',
+            'footer-running-right': '.running-footer .footer-right'
+        };
+        const elements = document.querySelectorAll(selectorMap[key]);
+        elements.forEach(elem => {
+            elem.addEventListener('input', () => {
+                localStorage.setItem(key, elem.innerHTML);
+            });
+        });
+    });
+}
 
-    // We look at each page and adjust the heights of the workspaces to fit it nicely into the page.
-    // The width and height of the page will now depend on the letter or a4 setting.
+
+// We look at each page and adjust the heights of the workspaces to fit it nicely into the page.
+// The width and height of the page will now depend on the letter or a4 setting.
 function adjustWorkspaceToFitPage({paperSize, margins}) {
+    console.log("*** Adjusting workspace to fit page size:", paperSize, "with margins:", margins);
+
+    // Toggle off workspace highlight if it is on, so it doesn't interfere with resizing
+    const highlightWorkspaceCheckbox = document.getElementById("highlight-workspace-checkbox");
+    const wasHighlighted = highlightWorkspaceCheckbox && highlightWorkspaceCheckbox.checked;
+    if (wasHighlighted) {
+        toggleWorkspaceHighlight(false);
+    }
+
     let paperWidth, paperHeight;
     if (paperSize === 'a4' || document.body.classList.contains('a4')) {
         console.log("Setting page size to A4");
@@ -796,6 +675,11 @@ function adjustWorkspaceToFitPage({paperSize, margins}) {
         page.style.width = "";
     });
     console.log("Set page sizes to content area of paper size.");
+
+    // Reset the highlight workspace checkbox state
+    if (wasHighlighted) {
+        toggleWorkspaceHighlight(true);
+    }
 }
 
 // Helper functions for calculating heights and workspace sizes
@@ -855,6 +739,7 @@ function getElemWorkspaceHeight(elem) {
 
 // Functions for finding the optimal page breaks
 function findPageBreaks(rows, pageHeight) {
+    console.log("*** Finding page breaks for", rows.length, "rows with page height:", pageHeight);
     // An array for the page breaks.  The nth element will be the index of the last row on page n.
     let pageBreaks = [];
     // An array for the minimum cost possible for rows i to the end.
@@ -901,7 +786,9 @@ function findPageBreaks(rows, pageHeight) {
     return pageBreaks;
 }
 
+// Function to set CSS variables and @page rules for page geometry.  This will be called whenever the paper size or margins change (in practice, only when page size changes, since margins are fixed for now).
 function setPageGeometryCSS({paperSize, margins}) {
+    console.log("*** Setting page geometry CSS for paper size:", paperSize, "with margins:", margins);
     // Remove any existing geometry CSS to avoid duplicates
     const existingStyle = document.getElementById("page-geometry-css");
     if (existingStyle) {
@@ -948,7 +835,6 @@ function toggleWorkspaceHighlight(isChecked) {
                 original.classList.add('original-workspace');
                 const originalHeight = workspace.getAttribute('data-space') || '0px';
                 original.setAttribute('title', 'Author-specified workspace height (' + originalHeight + ')');
-                console.log("setting original workspace height for", workspace);
                 // Use the data-space attribute for height of original workspace
                 original.style.height = originalHeight;
                 // insert original div before the workspace content
@@ -964,55 +850,24 @@ function toggleWorkspaceHighlight(isChecked) {
         }
     } else {
         document.body.classList.remove("highlight-workspace");
+        // Remove the original workspace divs.  We don't want to keep these in, as they interfere with changing page sizes and workspace heights.
+        document.querySelectorAll('.workspace-container').forEach(container => {
+            const workspace = container.querySelector('.workspace');
+            // Move the workspace out of the container
+            container.parentNode.insertBefore(workspace, container);
+            // Remove the container
+            container.remove();
+        });
     }
 }
 
-// Printout print preview and page setup
-window.addEventListener("load",function(event) {
-  // We condition on the existence of the papersize radio buttons, which only appear in the printout print preview.
-  if (document.querySelector('input[name="papersize"]')) {
-    // First, get the margins for pages to be passed around as needed.
-    const marginList = document.querySelector('section.worksheet, section.handout').getAttribute('data-margins').split(' ');
-    // Convert margin values to pixels if they are not already numbers
-    function toPixels(value) {
-        if (typeof value === "number") return value;
-        if (typeof value !== "string") return 0;
-        value = value.trim();
-        if (value.endsWith("px")) {
-            return parseFloat(value);
-        } else if (value.endsWith("in")) {
-            return Math.floor(parseFloat(value) * 96);
-        } else if (value.endsWith("cm")) {
-            return Math.floor(parseFloat(value) * 37.8);
-        } else if (value.endsWith("mm")) {
-            return Math.floor(parseFloat(value) * 3.78);
-        } else if (value.endsWith("pt")) {
-            return Math.floor(parseFloat(value) * (96 / 72));
-        } else {
-            // fallback: try to parse as px
-            return parseFloat(value) || 0;
-        }
-    }
-    const margins = {
-        top: toPixels(marginList[0] || "0.75in"), // Default to 0.75in if not specified
-        right: toPixels(marginList[1] || "0.75in"),
-        bottom: toPixels(marginList[2] || "0.75in"),
-        left: toPixels(marginList[3] || "0.75in")
-    }
-    // Get the papersize from localStorage or set it based on user's geographic region
+function getPaperSize() {
     let paperSize = localStorage.getItem("papersize");
     if (paperSize) {
-      const radio = document.querySelector(`input[name="papersize"][value="${paperSize}"]`);
-      if (radio) {
-        radio.checked = true;
-      }
-      // Set the papersize class on body
-      document.body.classList.remove("a4", "letter");
-      document.body.classList.add(paperSize);
-      setPageGeometryCSS({paperSize: paperSize, margins: margins});
+      return paperSize;
     } else {
-      // Try to set papersize based on user's geographic region
-      // Default to 'letter' for North and South America, 'a4' elsewhere
+        // Try to set papersize based on user's geographic region
+        // Default to 'letter' for North and South America, 'a4' elsewhere
         try {
           fetch('https://ipapi.co/json/')
             .then(response => response.json())
@@ -1037,69 +892,231 @@ window.addEventListener("load",function(event) {
           const radio = document.querySelector(`input[name="papersize"][value="letter"]`);
           if (radio) radio.checked = true;
         }
-      //NB: the default papersize is set to 'letter' in the body class list.
     }
-    const papersizeRadios = document.querySelectorAll('input[name="papersize"]');
-    papersizeRadios.forEach(radio => {
-      radio.addEventListener('change', function() {
-        if (this.checked) {
-          document.body.classList.remove("a4", "letter");
-          document.body.classList.add(this.value);
-          localStorage.setItem("papersize", this.value);
-          console.log("Setting papersize to", this.value);
+    return paperSize || "letter";
+}
 
-          // If the "highlight workspace" checkbox was already checked, then we should restart the process by reloading the page.  Specifically, we run into issues when there are .workspace-container divs already present.
-          if (document.querySelector(".workspace-container")) {
-            console.log("Reloading page to apply new papersize with workspace highlight enabled.");
-            window.location.reload();
-            return;
-          } else {
-            // Otherwise, we can just adjust the workspace heights to fit the new paper size.
-            console.log("Adjusting workspace heights to fit new papersize.");
-            adjustWorkspaceToFitPage({paperSize: this.value, margins: margins});
-            setPageGeometryCSS({paperSize: this.value, margins: margins});
-          }
-        }
-      });
-    });
+// Function to load the printout section and switch to print stylesheet.  This will run whenever a user clicks on a print preview link (which adds ?printpreview=sectionID to the URL).
+async function loadPrintout(printableSectionID) {
 
-    // Open all details elements (knowls) on the page
-    var born_hidden_knowls = document.querySelectorAll('details');
-    console.log("born_hidden_knowls", born_hidden_knowls);
-    born_hidden_knowls.forEach(function(detail) {
-        detail.open = true;
-    });
-    // If the printout has authored pages, there will be at least one .onepage element.
-    if (document.querySelector('.onepage')) {
-        adjustPrintoutPages();
-        /* not the right way:  need to figure out what this needs to wait for */
-        //window.setTimeout(adjustPrintoutPages, 1000);
-    } else {
-        createPrintoutPages(margins);
-    }
-    // After pages are set up, we adjust the workspace heights to fit the page (based on the paper size).
-    adjustWorkspaceToFitPage({paperSize: paperSize, margins: margins});
-
-    console.log("finished adjusting workspace");
-
-
-    // Get the 'highlight workspace' checkbox state from localStorage or set it to false by default
-    const highlightWorkspaceCheckbox = document.getElementById("highlight-workspace-checkbox");
-    if (highlightWorkspaceCheckbox) {
-        highlightWorkspaceCheckbox.checked = localStorage.getItem("highlightWorkspace") === "true";
-        highlightWorkspaceCheckbox.addEventListener("change", function() {
-            localStorage.setItem("highlightWorkspace", this.checked);
-            toggleWorkspaceHighlight(this.checked);
+    // Switch to print-worksheet.css for print preview
+    const themeStylesheetLink = document.querySelector('link[rel="stylesheet"][href*="theme"]');
+    // get the href of the theme stylesheet link
+    const themeStylesheetHref = themeStylesheetLink ? themeStylesheetLink.getAttribute('href') : null;
+    if (themeStylesheetHref) {
+        // replace 'theme.css' with 'print-worksheet.css' in the href
+        const printStylesheetHref = themeStylesheetHref.replace(/theme.*\.css/, 'print-worksheet.css');
+        // update the href of the theme stylesheet link
+        themeStylesheetLink.setAttribute('href', printStylesheetHref);
+        // Wait for the new stylesheet to load.  This is important to ensure the styles are applied before the calling function tries to compute workspace sizes.
+        await new Promise((resolve) => {
+            themeStylesheetLink.addEventListener('load', resolve, { once: true });
         });
-        // Initial toggle to apply the highlight class if checked
-        toggleWorkspaceHighlight(highlightWorkspaceCheckbox.checked);
     }
 
+    // Find the section with this ID
+    const printableSection = document.getElementById(printableSectionID);
+    if (!printableSection) {
+        console.error("No section found with ID:", printableSectionID);
+        return;
+    }
+    // Remove any existing sections from .ptx-content and add only the printable section
+    const ptxContent = document.querySelector('.ptx-content');
+    const existingSections = ptxContent.querySelectorAll(':scope > section');
+    existingSections.forEach(sec => ptxContent.removeChild(sec));
+    ptxContent.appendChild(printableSection);
+}
 
+// Function to redo solutions details to divs with summary as title
+function rewriteSolutions() {
+    var born_hidden_knowls = document.querySelectorAll('.worksheet details, .handout details');
+    born_hidden_knowls.forEach(function(detail) {
+        const summary = detail.querySelector('summary');
+        const content = detail.innerHTML.replace(summary.outerHTML, '');
+        const div = document.createElement('div');
+        div.classList = detail.classList;
+        if (summary) {
+            const title = document.createElement('h5');
+            title.innerHTML = summary.innerHTML;
+            div.appendChild(title);
+        }
+        const body = document.createElement('div');
+        body.innerHTML = content;
+        div.appendChild(body);
+        detail.parentNode.replaceChild(div, detail);
+    });
+}
 
-        // Not sure why this is here:
-      window.setTimeout(urlattribute, 1500);
-  }
+// Utility to convert various CSS length units to pixels
+function toPixels(value) {
+    if (typeof value === "number") return value;
+    if (typeof value !== "string") return 0;
+    value = value.trim();
+    if (value.endsWith("px")) {
+        return parseFloat(value);
+    } else if (value.endsWith("in")) {
+        return Math.floor(parseFloat(value) * 96);
+    } else if (value.endsWith("cm")) {
+        return Math.floor(parseFloat(value) * 37.8);
+    } else if (value.endsWith("mm")) {
+        return Math.floor(parseFloat(value) * 3.78);
+    } else if (value.endsWith("pt")) {
+        return Math.floor(parseFloat(value) * (96 / 72));
+    } else {
+        // fallback: try to parse as px
+        return parseFloat(value) || 0;
+    }
+}
+
+// Event listener for page load to handle print preview setup
+window.addEventListener("DOMContentLoaded", async function(event) {
+    const urlParams = new URLSearchParams(window.location.search);
+    // We condition on the existence of the papersize radio buttons, which only appear in the printout print preview.
+    if (urlParams.has("printpreview")) {
+        const printableSectionID = urlParams.get("printpreview");
+        await loadPrintout(printableSectionID);
+
+        // First, get the margins for pages to be passed around as needed.
+        const marginList = document.querySelector('section.worksheet, section.handout').getAttribute('data-margins').split(' ');
+        // Convert margin values to pixels if they are not already numbers
+        const margins = {
+            top: toPixels(marginList[0] || "0.75in"), // Default to 0.75in if not specified
+            right: toPixels(marginList[1] || "0.75in"),
+            bottom: toPixels(marginList[2] || "0.75in"),
+            left: toPixels(marginList[3] || "0.75in")
+        }
+
+        // Transform all solutions details elements to divs with the summary as a title
+        rewriteSolutions();
+
+        // Get the papersize from localStorage or set it based on user's geographic region.  This will always return a value (defaulting to 'letter' if all else fails).
+        let paperSize = getPaperSize();
+        if (paperSize) {
+        const radio = document.querySelector(`input[name="papersize"][value="${paperSize}"]`);
+        if (radio) {
+            radio.checked = true;
+        }
+        // Set the papersize class on body
+        document.body.classList.remove("a4", "letter");
+        document.body.classList.add(paperSize);
+        setPageGeometryCSS({paperSize: paperSize, margins: margins});
+        } else {
+            console.warning("Bug: paperSize should always have a value here.");
+        }
+        // Add event listeners to the papersize radio buttons to handle changes
+        const papersizeRadios = document.querySelectorAll('input[name="papersize"]');
+        papersizeRadios.forEach(radio => {
+            radio.addEventListener('change', function() {
+                if (this.checked) {
+                    document.body.classList.remove("a4", "letter");
+                    document.body.classList.add(this.value);
+                    localStorage.setItem("papersize", this.value);
+                    setPageGeometryCSS({paperSize: this.value, margins: margins});
+                    adjustWorkspaceToFitPage({paperSize: this.value, margins: margins});
+                }
+            });
+        });
+
+        // Add event listeners to the hide hints/answers/solutions checkboxes
+        for (const solutionType of ["hint", "answer", "solution"]) {
+            const checkbox = document.getElementById(`hide-${solutionType}-checkbox`);
+            if (checkbox) {
+                const storageKey = `hide-${solutionType}`;
+                // by default, hide answer and solution divs
+                if (solutionType === "answer" || solutionType === "solution") {
+                    if (!localStorage.getItem(storageKey)) {
+                        checkbox.checked = true;
+                        localStorage.setItem(storageKey, "true");
+                    }
+                }
+                // Now adjust based on local storage
+                // set visibility based on current checkbox state
+                checkbox.checked = localStorage.getItem(storageKey) === "true";
+                document.querySelectorAll(`div.${solutionType}`).forEach(elem => {
+                    // add hidden to class list
+                    if (checkbox.checked) {
+                        elem.classList.add("hidden");
+                    } else {
+                        elem.classList.remove("hidden");
+                    }
+                });
+                // Add event listener to toggle visibility
+                checkbox.addEventListener("change", function() {
+                    localStorage.setItem(storageKey, this.checked);
+                    // toggle visibility of solution divs
+                    document.querySelectorAll(`div.${solutionType}`).forEach(elem => {
+                        if (checkbox.checked) {
+                            elem.classList.add("hidden");
+                        } else {
+                            elem.classList.remove("hidden");
+                        }
+                        //adjustPrintoutPages();
+                        adjustWorkspaceToFitPage({paperSize: paperSize, margins: margins});
+                    });
+                });
+            }
+        }
+
+        // Finally, with everything set up, we create or adjust the printout pages as needed.
+
+        // If the printout has authored pages, there will be at least one .onepage element.
+        if (document.querySelector('.onepage')) {
+            adjustPrintoutPages();
+        } else {
+            createPrintoutPages(margins);
+        }
+
+        // Add headers and footers to all pages in the printout
+        addHeadersAndFootersToPrintout();
+
+        // Add event listeners to the print header/footer checkboxes
+        for (const hf of ["first-page-header", "running-header", "first-page-footer", "running-footer"]) {
+            const checkbox = document.getElementById(`print-${hf}-checkbox`);
+            if (checkbox) {
+                // set visibility based on current checkbox state
+                checkbox.checked = localStorage.getItem(`print-${hf}`) === "true";
+                document.querySelectorAll(`.${hf}`).forEach(elem => {
+                    // add hidden to class list
+                    if (checkbox.checked) {
+                        elem.classList.remove("hidden");
+                    } else {
+                        elem.classList.add("hidden");
+                    }
+                });
+                // Add event listener to toggle visibility
+                checkbox.addEventListener("change", function() {
+                    localStorage.setItem(`print-${hf}`, this.checked);
+                    // toggle visibility of header/footer divs
+                    document.querySelectorAll(`.${hf}`).forEach(elem => {
+                        if (checkbox.checked) {
+                            elem.classList.remove("hidden");
+                        } else {
+                            elem.classList.add("hidden");
+                        }
+                        adjustWorkspaceToFitPage({paperSize: paperSize, margins: margins});
+                    });
+                });
+            }
+        }
+
+        // After pages are set up, we adjust the workspace heights to fit the page (based on the paper size).
+        adjustWorkspaceToFitPage({paperSize: paperSize, margins: margins});
+
+        // Get the 'highlight workspace' checkbox state from localStorage or set it to false by default
+        // NB we need to do this after the adjustment of workspace heights so that the additional original workspace divs don't throw off the calculations when the page is reloaded.
+        const highlightWorkspaceCheckbox = document.getElementById("highlight-workspace-checkbox");
+        if (highlightWorkspaceCheckbox) {
+            highlightWorkspaceCheckbox.checked = localStorage.getItem("highlightWorkspace") === "true";
+            highlightWorkspaceCheckbox.addEventListener("change", function() {
+                localStorage.setItem("highlightWorkspace", this.checked);
+                toggleWorkspaceHighlight(this.checked);
+            });
+            // Initial toggle to apply the highlight class if checked
+            toggleWorkspaceHighlight(highlightWorkspaceCheckbox.checked);
+        }
+
+        console.log("finished adjusting workspace");
+    }
 });
 
 

_static/webpack_static_imports.json

@@ -1 +1 @@
-{"js":["prefix-runtime.fc0e080e84d54281.bundle.js","prefix-723.3e6434f80549315a.bundle.js","prefix-runestone.e2abc79debce15fd.bundle.js"],"css":["prefix-723.3bccd435914aa0ff.css","prefix-runestone.6ec5960970d8b364.css"]}
+{"js":["prefix-runtime.0d5f811896ddeac1.bundle.js","prefix-723.3e6434f80549315a.bundle.js","prefix-runestone.e2abc79debce15fd.bundle.js"],"css":["prefix-723.3bccd435914aa0ff.css","prefix-runestone.6ec5960970d8b364.css"]}

_static/webpack_static_imports.xml

@@ -1,7 +1,7 @@
 <?xml version="1.0" ?>
 <all>
 	<js type="list">
-		<item type="str">prefix-runtime.fc0e080e84d54281.bundle.js</item>
+		<item type="str">prefix-runtime.0d5f811896ddeac1.bundle.js</item>
 		<item type="str">prefix-723.3e6434f80549315a.bundle.js</item>
 		<item type="str">prefix-runestone.e2abc79debce15fd.bundle.js</item>
 	</js>
@@ -10,5 +10,5 @@
 		<item type="str">prefix-runestone.6ec5960970d8b364.css</item>
 	</css>
 	<cdn-url type="str">https://runestone.academy/cdn/runestone/</cdn-url>
-	<version type="str">7.11.11</version>
+	<version type="str">7.11.13</version>
 </all>

backmatter-2.html

@@ -62,7 +62,7 @@ window.MathJax = {
       "[pretext]/mathjaxknowl3.js"
     ],
     "paths": {
-      "pretext": "_static/pretext/js/lib"
+      "pretext": "_static/pretext/js"
     }
   },
   "startup": {
@@ -79,7 +79,7 @@ window.MathJax = {
 <meta property="og:type" content="book">
 <meta property="book:title" content="Math 1044 Notes">
 <meta property="book:author" content="Andy Eisenberg">
-<script src="_static/pretext/js/lib/jquery.min.js"></script><script src="_static/pretext/js/lib/jquery.sticky.js"></script><script src="_static/pretext/js/lib/jquery.espy.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><script src="_static/pretext/js/user_preferences.js"></script><!--** eBookCongig is necessary to configure interactive       **-->
+<script src="_static/pretext/js/jquery.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><!--** eBookCongig is necessary to configure interactive       **-->
 <!--** Runestone components to run locally in reader's browser **-->
 <!--** No external communication:                              **-->
 <!--**     log level is 0, Runestone Services are disabled     **-->
@@ -101,16 +101,16 @@ eBookConfig.allow_pairs = false;
 eBookConfig.enableScratchAC = false;
 eBookConfig.build_info = "";
 eBookConfig.python3 = null;
-eBookConfig.runestone_version = '7.11.11';
+eBookConfig.runestone_version = '7.11.13';
 eBookConfig.jobehost = '';
 eBookConfig.proxyuri_runs = '';
 eBookConfig.proxyuri_files = '';
 eBookConfig.enable_chatcodes =  false;
 </script>
 <!--*** Runestone Services ***-->
-<script src="_static/prefix-runtime.fc0e080e84d54281.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
+<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
 <link rel="stylesheet" type="text/css" href="_static/prefix-runestone.6ec5960970d8b364.css">
-<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/lib/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
+<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
 </script>
 </head>
 <body class="pretext book ignore-math">
@@ -151,6 +151,9 @@ eBookConfig.enable_chatcodes =  false;
 \DeclareMathOperator{\E}{E}
 \DeclareMathOperator{\Var}{Var}
 \DeclareMathOperator{\Cov}{Cov}
+\newcommand{\L}{\mathcal{L}}
+
+\newcommand{\est}{\widehat}
 \newcommand{\lt}{&lt;}
 \newcommand{\gt}{&gt;}
 \newcommand{\amp}{&amp;}
@@ -244,12 +247,16 @@ eBookConfig.enable_chatcodes =  false;
 <div class="toc-title-box"><a href="ch-Confidence-Intervals.html" class="internal"><span class="codenumber">4</span> <span class="title">Confidence Intervals</span></a></div>
 <ul class="structural toc-item-list">
 <li class="toc-item toc-section">
-<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Central Limit Theorem</span></a></div>
-<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
+<div class="toc-title-box"><a href="sec-Likelihood.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Likelihood</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Likelihood.html#sec-Likelihood-20" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
 </li>
 <li class="toc-item toc-section">
-<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Confidence Intervals</span></a></div>
-<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
+<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Central Limit Theorem</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.3</span> <span class="title">Confidence Intervals</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.3</span> <span class="title">Exercises</span></a></div></li></ul>
 </li>
 </ul>
 </li>

backmatter.html

@@ -62,7 +62,7 @@ window.MathJax = {
       "[pretext]/mathjaxknowl3.js"
     ],
     "paths": {
-      "pretext": "_static/pretext/js/lib"
+      "pretext": "_static/pretext/js"
     }
   },
   "startup": {
@@ -79,7 +79,7 @@ window.MathJax = {
 <meta property="og:type" content="book">
 <meta property="book:title" content="Math 1044 Notes">
 <meta property="book:author" content="Andy Eisenberg">
-<script src="_static/pretext/js/lib/jquery.min.js"></script><script src="_static/pretext/js/lib/jquery.sticky.js"></script><script src="_static/pretext/js/lib/jquery.espy.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><script src="_static/pretext/js/user_preferences.js"></script><!--** eBookCongig is necessary to configure interactive       **-->
+<script src="_static/pretext/js/jquery.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><!--** eBookCongig is necessary to configure interactive       **-->
 <!--** Runestone components to run locally in reader's browser **-->
 <!--** No external communication:                              **-->
 <!--**     log level is 0, Runestone Services are disabled     **-->
@@ -101,16 +101,16 @@ eBookConfig.allow_pairs = false;
 eBookConfig.enableScratchAC = false;
 eBookConfig.build_info = "";
 eBookConfig.python3 = null;
-eBookConfig.runestone_version = '7.11.11';
+eBookConfig.runestone_version = '7.11.13';
 eBookConfig.jobehost = '';
 eBookConfig.proxyuri_runs = '';
 eBookConfig.proxyuri_files = '';
 eBookConfig.enable_chatcodes =  false;
 </script>
 <!--*** Runestone Services ***-->
-<script src="_static/prefix-runtime.fc0e080e84d54281.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
+<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
 <link rel="stylesheet" type="text/css" href="_static/prefix-runestone.6ec5960970d8b364.css">
-<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/lib/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
+<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
 </script>
 </head>
 <body class="pretext book ignore-math">
@@ -151,6 +151,9 @@ eBookConfig.enable_chatcodes =  false;
 \DeclareMathOperator{\E}{E}
 \DeclareMathOperator{\Var}{Var}
 \DeclareMathOperator{\Cov}{Cov}
+\newcommand{\L}{\mathcal{L}}
+
+\newcommand{\est}{\widehat}
 \newcommand{\lt}{&lt;}
 \newcommand{\gt}{&gt;}
 \newcommand{\amp}{&amp;}
@@ -244,12 +247,16 @@ eBookConfig.enable_chatcodes =  false;
 <div class="toc-title-box"><a href="ch-Confidence-Intervals.html" class="internal"><span class="codenumber">4</span> <span class="title">Confidence Intervals</span></a></div>
 <ul class="structural toc-item-list">
 <li class="toc-item toc-section">
-<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Central Limit Theorem</span></a></div>
-<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
+<div class="toc-title-box"><a href="sec-Likelihood.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Likelihood</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Likelihood.html#sec-Likelihood-20" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
 </li>
 <li class="toc-item toc-section">
-<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Confidence Intervals</span></a></div>
-<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
+<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Central Limit Theorem</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.3</span> <span class="title">Confidence Intervals</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.3</span> <span class="title">Exercises</span></a></div></li></ul>
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ch-Confidence-Intervals.html

@@ -62,7 +62,7 @@ window.MathJax = {
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     ],
     "paths": {
-      "pretext": "_static/pretext/js/lib"
+      "pretext": "_static/pretext/js"
     }
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@@ -79,7 +79,7 @@ window.MathJax = {
 <meta property="og:type" content="book">
 <meta property="book:title" content="Math 1044 Notes">
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+<script src="_static/pretext/js/jquery.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><!--** eBookCongig is necessary to configure interactive       **-->
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+<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
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+<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
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+<button id="light-dark-button" class="light-dark-button button" title="Dark Mode"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe51c;</span><span class="name">Dark Mode</span></button></span><span class="treebuttons"><a class="previous-button button" href="sec-Covariance.html" title="Previous"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe5cb;</span><span class="name">Prev</span></a><a class="up-button button" href="my-great-book.html" title="Up"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe5ce;</span><span class="name">Up</span></a><a class="next-button button" href="sec-Likelihood.html" title="Next"><span class="name">Next</span><span class="icon material-symbols-outlined" aria-hidden="true">&#xe5cc;</span></a></span>
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 \DeclareMathOperator{\E}{E}
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+
+\newcommand{\est}{\widehat}
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 \newcommand{\gt}{&gt;}
 \newcommand{\amp}{&amp;}
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+<div class="toc-title-box"><a href="sec-Likelihood.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Likelihood</span></a></div>
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+<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Central Limit Theorem</span></a></div>
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+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.3</span> <span class="title">Confidence Intervals</span></a></div>
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-<li><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Confidence Intervals</span></a></li>
+<li><a href="sec-Likelihood.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Likelihood</span></a></li>
+<li><a href="sec-CLT.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Central Limit Theorem</span></a></li>
+<li><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.3</span> <span class="title">Confidence Intervals</span></a></li>
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+<a class="previous-button button" href="sec-Covariance.html" title="Previous"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe5cb;</span><span class="name">Prev</span></a><a class="top-button button" href="#" title="Top"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe5ce;</span><span class="name">Top</span></a><a class="next-button button" href="sec-Likelihood.html" title="Next"><span class="name">Next</span><span class="icon material-symbols-outlined" aria-hidden="true">&#xe5cc;</span></a>
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ch-Expected-Value.html

@@ -62,7 +62,7 @@ window.MathJax = {
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     ],
     "paths": {
-      "pretext": "_static/pretext/js/lib"
+      "pretext": "_static/pretext/js"
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 <meta property="book:title" content="Math 1044 Notes">
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+<script src="_static/pretext/js/jquery.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><!--** eBookCongig is necessary to configure interactive       **-->
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 <body class="pretext book ignore-math">
@@ -151,6 +151,9 @@ eBookConfig.enable_chatcodes =  false;
 \DeclareMathOperator{\E}{E}
 \DeclareMathOperator{\Var}{Var}
 \DeclareMathOperator{\Cov}{Cov}
+\newcommand{\L}{\mathcal{L}}
+
+\newcommand{\est}{\widehat}
 \newcommand{\lt}{&lt;}
 \newcommand{\gt}{&gt;}
 \newcommand{\amp}{&amp;}
@@ -244,12 +247,16 @@ eBookConfig.enable_chatcodes =  false;
 <div class="toc-title-box"><a href="ch-Confidence-Intervals.html" class="internal"><span class="codenumber">4</span> <span class="title">Confidence Intervals</span></a></div>
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 <li class="toc-item toc-section">
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+<div class="toc-title-box"><a href="sec-Likelihood.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Likelihood</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Likelihood.html#sec-Likelihood-20" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
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+<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Central Limit Theorem</span></a></div>
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+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.3</span> <span class="title">Confidence Intervals</span></a></div>
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@@ -62,7 +62,7 @@ window.MathJax = {
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+      "pretext": "_static/pretext/js"
     }
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@@ -79,7 +79,7 @@ window.MathJax = {
 <meta property="og:type" content="book">
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+<script src="_static/pretext/js/jquery.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><!--** eBookCongig is necessary to configure interactive       **-->
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 eBookConfig.python3 = null;
-eBookConfig.runestone_version = '7.11.11';
+eBookConfig.runestone_version = '7.11.13';
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+<li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Conditional-Probability.html#exercises-Conditional-Probability" class="internal"><span class="codenumber">1.3.3</span> <span class="title">Exercises</span></a></div></li>
+</ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Independent-Events.html" class="internal"><span class="codenumber">1.4</span> <span class="title">Independent Events</span></a></div>
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+</ul>
+</li>
+<li class="toc-item toc-chapter">
+<div class="toc-title-box"><a href="ch-Random-Variables.html" class="internal"><span class="codenumber">2</span> <span class="title">Random Variables</span></a></div>
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+<div class="toc-title-box"><a href="sec-Discrete-RVs.html" class="internal"><span class="codenumber">2.1</span> <span class="title">Discrete Random Variables</span></a></div>
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+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Discrete-RVs.html#subsec-Discrete-RVs" class="internal"><span class="codenumber">2.1.1</span> <span class="title">Discrete Random Variables</span></a></div></li>
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Discrete-RVs.html#subsec-binomial-distribution" class="internal"><span class="codenumber">2.1.2</span> <span class="title">The Binomial Distribution</span></a></div></li>
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Discrete-RVs.html#subsec-geometric-distribution" class="internal"><span class="codenumber">2.1.3</span> <span class="title">Geometric Distribution</span></a></div></li>
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Discrete-RVs.html#subsec-poisson-distribution" class="internal"><span class="codenumber">2.1.4</span> <span class="title">Poisson Distribution</span></a></div></li>
+<li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Discrete-RVs.html#exercises-Discrete-RVs" class="internal"><span class="codenumber">2.1.5</span> <span class="title">Exercises</span></a></div></li>
+</ul>
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+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Continuous-RVs.html" class="internal"><span class="codenumber">2.2</span> <span class="title">Continuous Random Variables</span></a></div>
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+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Continuous-RVs.html#subsec-cdf" class="internal"><span class="codenumber">2.2.2</span> <span class="title">Cumulative Distribution Functions</span></a></div></li>
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Continuous-RVs.html#subsec-exponential-distribution" class="internal"><span class="codenumber">2.2.3</span> <span class="title">The Exponential Distribution</span></a></div></li>
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Continuous-RVs.html#subsec-normal-distribution" class="internal"><span class="codenumber">2.2.4</span> <span class="title">Normal Distribution</span></a></div></li>
+<li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Continuous-RVs.html#exercises-Continuous-RVs" class="internal"><span class="codenumber">2.2.5</span> <span class="title">Exercises</span></a></div></li>
+</ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Joint-Distributions.html" class="internal"><span class="codenumber">2.3</span> <span class="title">Joint Distributions</span></a></div>
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+</li>
+</ul>
+</li>
+<li class="toc-item toc-chapter">
+<div class="toc-title-box"><a href="ch-Expected-Value.html" class="internal"><span class="codenumber">3</span> <span class="title">Expected Value and Variance</span></a></div>
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+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Expected-Value.html#subsec-discrete-EV" class="internal"><span class="codenumber">3.1.1</span> <span class="title">Discrete Expected Value</span></a></div></li>
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Expected-Value.html#subsec-continuous-EV" class="internal"><span class="codenumber">3.1.2</span> <span class="title">Continuous Expected Value</span></a></div></li>
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Expected-Value.html#subsec-linearity-EV" class="internal"><span class="codenumber">3.1.3</span> <span class="title">Linearity of Expected Value</span></a></div></li>
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+<li class="toc-item toc-section">
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+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.3</span> <span class="title">Confidence Intervals</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.3</span> <span class="title">Exercises</span></a></div></li></ul>
 </li>
 </ul>
 </li>

ch-Probability.html

@@ -62,7 +62,7 @@ window.MathJax = {
       "[pretext]/mathjaxknowl3.js"
     ],
     "paths": {
-      "pretext": "_static/pretext/js/lib"
+      "pretext": "_static/pretext/js"
     }
   },
   "startup": {
@@ -79,7 +79,7 @@ window.MathJax = {
 <meta property="og:type" content="book">
 <meta property="book:title" content="Math 1044 Notes">
 <meta property="book:author" content="Andy Eisenberg">
-<script src="_static/pretext/js/lib/jquery.min.js"></script><script src="_static/pretext/js/lib/jquery.sticky.js"></script><script src="_static/pretext/js/lib/jquery.espy.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><script src="_static/pretext/js/user_preferences.js"></script><!--** eBookCongig is necessary to configure interactive       **-->
+<script src="_static/pretext/js/jquery.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><!--** eBookCongig is necessary to configure interactive       **-->
 <!--** Runestone components to run locally in reader's browser **-->
 <!--** No external communication:                              **-->
 <!--**     log level is 0, Runestone Services are disabled     **-->
@@ -101,16 +101,16 @@ eBookConfig.allow_pairs = false;
 eBookConfig.enableScratchAC = false;
 eBookConfig.build_info = "";
 eBookConfig.python3 = null;
-eBookConfig.runestone_version = '7.11.11';
+eBookConfig.runestone_version = '7.11.13';
 eBookConfig.jobehost = '';
 eBookConfig.proxyuri_runs = '';
 eBookConfig.proxyuri_files = '';
 eBookConfig.enable_chatcodes =  false;
 </script>
 <!--*** Runestone Services ***-->
-<script src="_static/prefix-runtime.fc0e080e84d54281.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
+<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
 <link rel="stylesheet" type="text/css" href="_static/prefix-runestone.6ec5960970d8b364.css">
-<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/lib/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
+<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
 </script>
 </head>
 <body class="pretext book ignore-math">
@@ -151,6 +151,9 @@ eBookConfig.enable_chatcodes =  false;
 \DeclareMathOperator{\E}{E}
 \DeclareMathOperator{\Var}{Var}
 \DeclareMathOperator{\Cov}{Cov}
+\newcommand{\L}{\mathcal{L}}
+
+\newcommand{\est}{\widehat}
 \newcommand{\lt}{&lt;}
 \newcommand{\gt}{&gt;}
 \newcommand{\amp}{&amp;}
@@ -244,12 +247,16 @@ eBookConfig.enable_chatcodes =  false;
 <div class="toc-title-box"><a href="ch-Confidence-Intervals.html" class="internal"><span class="codenumber">4</span> <span class="title">Confidence Intervals</span></a></div>
 <ul class="structural toc-item-list">
 <li class="toc-item toc-section">
-<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Central Limit Theorem</span></a></div>
-<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
+<div class="toc-title-box"><a href="sec-Likelihood.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Likelihood</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Likelihood.html#sec-Likelihood-20" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
 </li>
 <li class="toc-item toc-section">
-<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Confidence Intervals</span></a></div>
-<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
+<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Central Limit Theorem</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.3</span> <span class="title">Confidence Intervals</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.3</span> <span class="title">Exercises</span></a></div></li></ul>
 </li>
 </ul>
 </li>

ch-Random-Variables.html

@@ -62,7 +62,7 @@ window.MathJax = {
       "[pretext]/mathjaxknowl3.js"
     ],
     "paths": {
-      "pretext": "_static/pretext/js/lib"
+      "pretext": "_static/pretext/js"
     }
   },
   "startup": {
@@ -79,7 +79,7 @@ window.MathJax = {
 <meta property="og:type" content="book">
 <meta property="book:title" content="Math 1044 Notes">
 <meta property="book:author" content="Andy Eisenberg">
-<script src="_static/pretext/js/lib/jquery.min.js"></script><script src="_static/pretext/js/lib/jquery.sticky.js"></script><script src="_static/pretext/js/lib/jquery.espy.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><script src="_static/pretext/js/user_preferences.js"></script><!--** eBookCongig is necessary to configure interactive       **-->
+<script src="_static/pretext/js/jquery.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><!--** eBookCongig is necessary to configure interactive       **-->
 <!--** Runestone components to run locally in reader's browser **-->
 <!--** No external communication:                              **-->
 <!--**     log level is 0, Runestone Services are disabled     **-->
@@ -101,16 +101,16 @@ eBookConfig.allow_pairs = false;
 eBookConfig.enableScratchAC = false;
 eBookConfig.build_info = "";
 eBookConfig.python3 = null;
-eBookConfig.runestone_version = '7.11.11';
+eBookConfig.runestone_version = '7.11.13';
 eBookConfig.jobehost = '';
 eBookConfig.proxyuri_runs = '';
 eBookConfig.proxyuri_files = '';
 eBookConfig.enable_chatcodes =  false;
 </script>
 <!--*** Runestone Services ***-->
-<script src="_static/prefix-runtime.fc0e080e84d54281.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
+<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
 <link rel="stylesheet" type="text/css" href="_static/prefix-runestone.6ec5960970d8b364.css">
-<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/lib/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
+<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
 </script>
 </head>
 <body class="pretext book ignore-math">
@@ -151,6 +151,9 @@ eBookConfig.enable_chatcodes =  false;
 \DeclareMathOperator{\E}{E}
 \DeclareMathOperator{\Var}{Var}
 \DeclareMathOperator{\Cov}{Cov}
+\newcommand{\L}{\mathcal{L}}
+
+\newcommand{\est}{\widehat}
 \newcommand{\lt}{&lt;}
 \newcommand{\gt}{&gt;}
 \newcommand{\amp}{&amp;}
@@ -244,12 +247,16 @@ eBookConfig.enable_chatcodes =  false;
 <div class="toc-title-box"><a href="ch-Confidence-Intervals.html" class="internal"><span class="codenumber">4</span> <span class="title">Confidence Intervals</span></a></div>
 <ul class="structural toc-item-list">
 <li class="toc-item toc-section">
-<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Central Limit Theorem</span></a></div>
-<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
+<div class="toc-title-box"><a href="sec-Likelihood.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Likelihood</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Likelihood.html#sec-Likelihood-20" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
 </li>
 <li class="toc-item toc-section">
-<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Confidence Intervals</span></a></div>
-<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
+<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Central Limit Theorem</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.3</span> <span class="title">Confidence Intervals</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.3</span> <span class="title">Exercises</span></a></div></li></ul>
 </li>
 </ul>
 </li>

front-colophon.html

@@ -62,7 +62,7 @@ window.MathJax = {
       "[pretext]/mathjaxknowl3.js"
     ],
     "paths": {
-      "pretext": "_static/pretext/js/lib"
+      "pretext": "_static/pretext/js"
     }
   },
   "startup": {
@@ -79,7 +79,7 @@ window.MathJax = {
 <meta property="og:type" content="book">
 <meta property="book:title" content="Math 1044 Notes">
 <meta property="book:author" content="Andy Eisenberg">
-<script src="_static/pretext/js/lib/jquery.min.js"></script><script src="_static/pretext/js/lib/jquery.sticky.js"></script><script src="_static/pretext/js/lib/jquery.espy.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><script src="_static/pretext/js/user_preferences.js"></script><!--** eBookCongig is necessary to configure interactive       **-->
+<script src="_static/pretext/js/jquery.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><!--** eBookCongig is necessary to configure interactive       **-->
 <!--** Runestone components to run locally in reader's browser **-->
 <!--** No external communication:                              **-->
 <!--**     log level is 0, Runestone Services are disabled     **-->
@@ -101,16 +101,16 @@ eBookConfig.allow_pairs = false;
 eBookConfig.enableScratchAC = false;
 eBookConfig.build_info = "";
 eBookConfig.python3 = null;
-eBookConfig.runestone_version = '7.11.11';
+eBookConfig.runestone_version = '7.11.13';
 eBookConfig.jobehost = '';
 eBookConfig.proxyuri_runs = '';
 eBookConfig.proxyuri_files = '';
 eBookConfig.enable_chatcodes =  false;
 </script>
 <!--*** Runestone Services ***-->
-<script src="_static/prefix-runtime.fc0e080e84d54281.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
+<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
 <link rel="stylesheet" type="text/css" href="_static/prefix-runestone.6ec5960970d8b364.css">
-<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/lib/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
+<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
 </script>
 </head>
 <body class="pretext book ignore-math">
@@ -151,6 +151,9 @@ eBookConfig.enable_chatcodes =  false;
 \DeclareMathOperator{\E}{E}
 \DeclareMathOperator{\Var}{Var}
 \DeclareMathOperator{\Cov}{Cov}
+\newcommand{\L}{\mathcal{L}}
+
+\newcommand{\est}{\widehat}
 \newcommand{\lt}{&lt;}
 \newcommand{\gt}{&gt;}
 \newcommand{\amp}{&amp;}
@@ -244,12 +247,16 @@ eBookConfig.enable_chatcodes =  false;
 <div class="toc-title-box"><a href="ch-Confidence-Intervals.html" class="internal"><span class="codenumber">4</span> <span class="title">Confidence Intervals</span></a></div>
 <ul class="structural toc-item-list">
 <li class="toc-item toc-section">
-<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Central Limit Theorem</span></a></div>
-<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
+<div class="toc-title-box"><a href="sec-Likelihood.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Likelihood</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Likelihood.html#sec-Likelihood-20" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
 </li>
 <li class="toc-item toc-section">
-<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Confidence Intervals</span></a></div>
-<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
+<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Central Limit Theorem</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.3</span> <span class="title">Confidence Intervals</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.3</span> <span class="title">Exercises</span></a></div></li></ul>
 </li>
 </ul>
 </li>

frontmatter.html

@@ -62,7 +62,7 @@ window.MathJax = {
       "[pretext]/mathjaxknowl3.js"
     ],
     "paths": {
-      "pretext": "_static/pretext/js/lib"
+      "pretext": "_static/pretext/js"
     }
   },
   "startup": {
@@ -79,7 +79,7 @@ window.MathJax = {
 <meta property="og:type" content="book">
 <meta property="book:title" content="Math 1044 Notes">
 <meta property="book:author" content="Andy Eisenberg">
-<script src="_static/pretext/js/lib/jquery.min.js"></script><script src="_static/pretext/js/lib/jquery.sticky.js"></script><script src="_static/pretext/js/lib/jquery.espy.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><script src="_static/pretext/js/user_preferences.js"></script><!--** eBookCongig is necessary to configure interactive       **-->
+<script src="_static/pretext/js/jquery.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><!--** eBookCongig is necessary to configure interactive       **-->
 <!--** Runestone components to run locally in reader's browser **-->
 <!--** No external communication:                              **-->
 <!--**     log level is 0, Runestone Services are disabled     **-->
@@ -101,16 +101,16 @@ eBookConfig.allow_pairs = false;
 eBookConfig.enableScratchAC = false;
 eBookConfig.build_info = "";
 eBookConfig.python3 = null;
-eBookConfig.runestone_version = '7.11.11';
+eBookConfig.runestone_version = '7.11.13';
 eBookConfig.jobehost = '';
 eBookConfig.proxyuri_runs = '';
 eBookConfig.proxyuri_files = '';
 eBookConfig.enable_chatcodes =  false;
 </script>
 <!--*** Runestone Services ***-->
-<script src="_static/prefix-runtime.fc0e080e84d54281.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
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+<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
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@@ -151,6 +151,9 @@ eBookConfig.enable_chatcodes =  false;
 \DeclareMathOperator{\E}{E}
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+\newcommand{\L}{\mathcal{L}}
+
+\newcommand{\est}{\widehat}
 \newcommand{\lt}{&lt;}
 \newcommand{\gt}{&gt;}
 \newcommand{\amp}{&amp;}
@@ -244,12 +247,16 @@ eBookConfig.enable_chatcodes =  false;
 <div class="toc-title-box"><a href="ch-Confidence-Intervals.html" class="internal"><span class="codenumber">4</span> <span class="title">Confidence Intervals</span></a></div>
 <ul class="structural toc-item-list">
 <li class="toc-item toc-section">
-<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Central Limit Theorem</span></a></div>
-<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
+<div class="toc-title-box"><a href="sec-Likelihood.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Likelihood</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Likelihood.html#sec-Likelihood-20" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
 </li>
 <li class="toc-item toc-section">
-<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Confidence Intervals</span></a></div>
-<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
+<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Central Limit Theorem</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.3</span> <span class="title">Confidence Intervals</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.3</span> <span class="title">Exercises</span></a></div></li></ul>
 </li>
 </ul>
 </li>
@@ -294,7 +301,7 @@ eBookConfig.enable_chatcodes =  false;
 <div class="author-name">Andy Eisenberg</div>
 <div class="author-info">Mathematics Department<br>Temple University</div>
 </div>
-<div class="date">January 29, 2026</div>
+<div class="date">February 10, 2026</div>
 <nav class="summary-links"><ul><li><a href="front-colophon.html" class="internal"><span class="title">Colophon</span></a></li></ul></nav><div class="autopermalink" data-description="Front Matter"><a href="#frontmatter" title="Copy heading and permalink for Front Matter" aria-label="Copy heading and permalink for Front Matter">🔗</a></div></section></div>
 <div id="ptx-content-footer" class="ptx-content-footer">
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index.html

@@ -2,7 +2,7 @@
 <html>
 <!--********************************************-->
 <!--*       Generated from PreTeXt source      *-->
-<!--*       on 2026-01-29T06:34:50-05:00       *-->
+<!--*       on 2026-02-10T07:44:10-05:00       *-->
 <!--*   A recent stable commit (2022-07-01):   *-->
 <!--* 6c761d3dba23af92cba35001c852aac04ae99a5f *-->
 <!--*                                          *-->

knowl/xref/example-exponential-MLE.html

@@ -0,0 +1,98 @@
+<!DOCTYPE html>
+<html lang="en-US" dir="ltr">
+<!--******************************************-->
+<!--*  Authored with PreTeXt                 *-->
+<!--*  pretextbook.org                       *-->
+<!--*  Theme: boulder                        *-->
+<!--*  Palette:                              *-->
+<!--******************************************-->
+
+<!--********************************************-->
+<!--*       Generated from PreTeXt source      *-->
+<!--*                                          *-->
+<!--*         https://pretextbook.org          *-->
+<!--*                                          *-->
+<!--********************************************-->
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
+<meta name="robots" content="noindex, nofollow">
+</head>
+<body class="ignore-math">
+<article class="example example-like"><h3 class="heading">
+<span class="type">Example</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.1.11</span><span class="period heading-divison-mark heading-divison-mark__period">.</span>
+</h3>
+<div class="para logical">
+<div class="para">Suppose we observe a cell and measure the time <span class="process-math">\(T\)</span> until a toxin molecule leaves the cell. Then <span class="process-math">\(T \sim \Exp(\lambda)\)</span> for some unknown rate parameter <span class="process-math">\(\lambda\text{:}\)</span>
+</div>
+<div class="displaymath process-math">
+\begin{gather*}
+f(t) = \lambda e^{-\lambda t}. 
+\end{gather*}
+</div>
+<div class="para">Suppose we observe a molecule leave the cell at <span class="process-math">\(t = 0.3\)</span> minutes. Then:</div>
+<div class="displaymath process-math">
+\begin{align*}
+L(\lambda) \amp = \lambda e^{-0.3\lambda} \\
+L'(\lambda) \amp = e^{-0.3\lambda} + \lambda e^{-0.3t} (-0.3) \\
+\amp = e^{-0.3\lambda}\left[ 1 - 0.3\lambda\right] 
+\end{align*}
+</div>
+<div class="para">The critical point is <span class="process-math">\(\lambda = \frac{1}{0.3} \approx 3.33\text{.}\)</span> Since <span class="process-math">\(\L' \gt 0\)</span> on <span class="process-math">\((0, 3.33)\)</span> and <span class="process-math">\(\L' \lt 0\)</span> on <span class="process-math">\((3.33, \infty)\text{,}\)</span> there is a global maximum at <span class="process-math">\(\lambda \approx 3.33\text{,}\)</span> which is therefore the MLE.</div>
+<div class="autopermalink" data-description="Paragraph"><a href="#example-exponential-MLE-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div> <div class="para">The specific time <span class="process-math">\(0.3\)</span> minutes doesn’t particularly matter in this calculation. Whatever the time <span class="process-math">\(t\text{,}\)</span> essentially the same calculation will result in a MLE of <span class="process-math">\(\lambda = 1/t\text{.}\)</span> But what if we collect multiple pieces of data?<div class="autopermalink" data-description="Paragraph"><a href="#example-exponential-MLE-1-2" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div> <figure class="table table-like"><figcaption><span class="type">Table</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.1.12<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span>Time Data<div class="autopermalink" data-description="Table 4.1.12: Time Data"><a href="#example-exponential-MLE-1-3" title="Copy heading and permalink for Table 4.1.12: Time Data" aria-label="Copy heading and permalink for Table 4.1.12: Time Data">🔗</a></div></figcaption><div class="tabular-box natural-width"><table class="tabular">
+<tr>
+<td class="c m b1 r0 l0 t0 lines">Molecule</td>
+<td class="c m b1 r0 l0 t0 lines">Waiting Time</td>
+<td class="c m b1 r0 l0 t0 lines">Rate Estimation</td>
+</tr>
+<tr>
+<td class="c m b0 r0 l0 t0 lines">1</td>
+<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(0.3\)</span></td>
+<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(3.33\)</span></td>
+</tr>
+<tr>
+<td class="c m b0 r0 l0 t0 lines">2</td>
+<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(0.8\)</span></td>
+<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(1.25\)</span></td>
+</tr>
+<tr>
+<td class="c m b0 r0 l0 t0 lines">3</td>
+<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(0.5\)</span></td>
+<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(2.00\)</span></td>
+</tr>
+<tr>
+<td class="c m b0 r0 l0 t0 lines">4</td>
+<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(0.6\)</span></td>
+<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(1.67\)</span></td>
+</tr>
+<tr>
+<td class="c m b0 r0 l0 t0 lines">5</td>
+<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(0.9\)</span></td>
+<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(1.11\)</span></td>
+</tr>
+</table></div></figure> <div class="para">How should take all of this data into account in our maximum likelihood estimation? We might consider taking the average of all of the separate rate estimations, which would give <span class="process-math">\(1.87\text{.}\)</span> Is this the most likely? We need some mathematical justification.<div class="autopermalink" data-description="Paragraph"><a href="#example-exponential-MLE-1-4" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div> <div class="para logical">
+<div class="para">To account for multiple, independent data points, we should multiply the probability densities for each in the creation of our likelihood function:</div>
+<div class="displaymath process-math">
+\begin{align*}
+\L(\lambda) \amp = \left(\lambda e^{-0.3\lambda}\right)\left(\lambda e^{-0.8\lambda}\right)\left(\lambda e^{-0.5\lambda}\right)\left(\lambda e^{-0.6\lambda}\right)\left(\lambda e^{-0.9\lambda}\right) \\
+\amp = \lambda^5 e^{-0.3\lambda - 0.8\lambda - 0.5\lambda - 0.6\lambda - 0.9\lambda } \\
+\amp = \lambda^5 e^{-3.1\lambda} 
+\end{align*}
+</div>
+<div class="para">Now we can find the maximum:</div>
+<div class="displaymath process-math">
+\begin{align*}
+\L'(\lambda) \amp = 5 \lambda^4 e^{-3.1\lambda} + \lambda^5 e^{-3.1\lambda} (-3.1) \\
+\amp = 5 \lambda^4 e^{-3.1\lambda} + \lambda^5 e^{-3.1\lambda} (-3.1) \\
+\amp = \lambda^4 e^{-3.1\lambda} \left[5 - 3.1\lambda \right] 
+\end{align*}
+</div>
+<div class="para">The only critical point is <span class="process-math">\(5/3.1 \approx 1.61\text{.}\)</span> Since <span class="process-math">\(\L' \gt 0\)</span> on <span class="process-math">\((0, 1.61)\)</span> and <span class="process-math">\(\L' \lt 0\)</span> on <span class="process-math">\((1.61, \infty)\text{,}\)</span> there is a global maximum at <span class="process-math">\(\lambda = 1.61\text{,}\)</span> which is therefore the MLE.</div>
+<div class="autopermalink" data-description="Paragraph"><a href="#example-exponential-MLE-1-5" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div> <div class="para">It may seem less clear how to generalize this calculation for other tables of data. Observe that the value <span class="process-math">\(3.1\)</span> is the sum of the five times in the table, so <span class="process-math">\(3.1/5\)</span> is the average time. The MLE turned out to be the reciprocal of the average time (just as the MLE with only one data point was the reciprocal of that one time). Notice that this does <em class="emphasis">not</em> match the guess we made previously of averaging the individual rate estimations for each data point.<div class="autopermalink" data-description="Paragraph"><a href="#example-exponential-MLE-1-6" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Example 4.1.11"><a href="#example-exponential-MLE" title="Copy heading and permalink for Example 4.1.11" aria-label="Copy heading and permalink for Example 4.1.11">🔗</a></div></article><span class="incontext"><a class="internal" href="sec-Likelihood.html#example-exponential-MLE">in-context</a></span>
+</body>
+</html>

knowl/xref/fact-MLE-binomial.html

@@ -0,0 +1,28 @@
+<!DOCTYPE html>
+<html lang="en-US" dir="ltr">
+<!--******************************************-->
+<!--*  Authored with PreTeXt                 *-->
+<!--*  pretextbook.org                       *-->
+<!--*  Theme: boulder                        *-->
+<!--*  Palette:                              *-->
+<!--******************************************-->
+
+<!--********************************************-->
+<!--*       Generated from PreTeXt source      *-->
+<!--*                                          *-->
+<!--*         https://pretextbook.org          *-->
+<!--*                                          *-->
+<!--********************************************-->
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
+<meta name="robots" content="noindex, nofollow">
+</head>
+<body class="ignore-math">
+<article class="fact theorem-like"><h3 class="heading">
+<span class="type">Fact</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.1.8</span><span class="period heading-divison-mark heading-divison-mark__period">.</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Binomial MLE.</span>
+</h3>
+<div class="para">If we see <span class="process-math">\(k\)</span> heads in <span class="process-math">\(n\)</span> coin flips, then the MLE of the bias <span class="process-math">\(p\)</span> is <span class="process-math">\(\frac{k}{n}\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#fact-MLE-binomial-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Fact 4.1.8: Binomial MLE"><a href="#fact-MLE-binomial" title="Copy heading and permalink for Fact 4.1.8: Binomial MLE" aria-label="Copy heading and permalink for Fact 4.1.8: Binomial MLE">🔗</a></div></article><span class="incontext"><a class="internal" href="sec-Likelihood.html#fact-MLE-binomial">in-context</a></span>
+</body>
+</html>

my-great-book.html

@@ -62,7 +62,7 @@ window.MathJax = {
       "[pretext]/mathjaxknowl3.js"
     ],
     "paths": {
-      "pretext": "_static/pretext/js/lib"
+      "pretext": "_static/pretext/js"
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@@ -79,7 +79,7 @@ window.MathJax = {
 <meta property="og:type" content="book">
 <meta property="book:title" content="Math 1044 Notes">
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+<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
 </script>
 </head>
 <body class="pretext book ignore-math">
@@ -151,6 +151,9 @@ eBookConfig.enable_chatcodes =  false;
 \DeclareMathOperator{\E}{E}
 \DeclareMathOperator{\Var}{Var}
 \DeclareMathOperator{\Cov}{Cov}
+\newcommand{\L}{\mathcal{L}}
+
+\newcommand{\est}{\widehat}
 \newcommand{\lt}{&lt;}
 \newcommand{\gt}{&gt;}
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@@ -244,12 +247,16 @@ eBookConfig.enable_chatcodes =  false;
 <div class="toc-title-box"><a href="ch-Confidence-Intervals.html" class="internal"><span class="codenumber">4</span> <span class="title">Confidence Intervals</span></a></div>
 <ul class="structural toc-item-list">
 <li class="toc-item toc-section">
-<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Central Limit Theorem</span></a></div>
-<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
+<div class="toc-title-box"><a href="sec-Likelihood.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Likelihood</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Likelihood.html#sec-Likelihood-20" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
 </li>
 <li class="toc-item toc-section">
-<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Confidence Intervals</span></a></div>
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+<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Central Limit Theorem</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.3</span> <span class="title">Confidence Intervals</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.3</span> <span class="title">Exercises</span></a></div></li></ul>
 </li>
 </ul>
 </li>

sec-CLT.html

@@ -62,7 +62,7 @@ window.MathJax = {
       "[pretext]/mathjaxknowl3.js"
     ],
     "paths": {
-      "pretext": "_static/pretext/js/lib"
+      "pretext": "_static/pretext/js"
     }
   },
   "startup": {
@@ -79,7 +79,7 @@ window.MathJax = {
 <meta property="og:type" content="book">
 <meta property="book:title" content="Math 1044 Notes">
 <meta property="book:author" content="Andy Eisenberg">
-<script src="_static/pretext/js/lib/jquery.min.js"></script><script src="_static/pretext/js/lib/jquery.sticky.js"></script><script src="_static/pretext/js/lib/jquery.espy.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><script src="_static/pretext/js/user_preferences.js"></script><!--** eBookCongig is necessary to configure interactive       **-->
+<script src="_static/pretext/js/jquery.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><!--** eBookCongig is necessary to configure interactive       **-->
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 eBookConfig.enableScratchAC = false;
 eBookConfig.build_info = "";
 eBookConfig.python3 = null;
-eBookConfig.runestone_version = '7.11.11';
+eBookConfig.runestone_version = '7.11.13';
 eBookConfig.jobehost = '';
 eBookConfig.proxyuri_runs = '';
 eBookConfig.proxyuri_files = '';
 eBookConfig.enable_chatcodes =  false;
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+<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
 <link rel="stylesheet" type="text/css" href="_static/prefix-runestone.6ec5960970d8b364.css">
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+<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
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 <body class="pretext book ignore-math">
@@ -135,7 +135,7 @@ eBookConfig.enable_chatcodes =  false;
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-<button id="light-dark-button" class="light-dark-button button" title="Dark Mode"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe51c;</span><span class="name">Dark Mode</span></button></span><span class="treebuttons"><a class="previous-button button" href="ch-Confidence-Intervals.html" title="Previous"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe5cb;</span><span class="name">Prev</span></a><a class="up-button button" href="ch-Confidence-Intervals.html" title="Up"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe5ce;</span><span class="name">Up</span></a><a class="next-button button" href="sec-Confidence-Intervals.html" title="Next"><span class="name">Next</span><span class="icon material-symbols-outlined" aria-hidden="true">&#xe5cc;</span></a></span>
+<button id="light-dark-button" class="light-dark-button button" title="Dark Mode"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe51c;</span><span class="name">Dark Mode</span></button></span><span class="treebuttons"><a class="previous-button button" href="sec-Likelihood.html" title="Previous"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe5cb;</span><span class="name">Prev</span></a><a class="up-button button" href="ch-Confidence-Intervals.html" title="Up"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe5ce;</span><span class="name">Up</span></a><a class="next-button button" href="sec-Confidence-Intervals.html" title="Next"><span class="name">Next</span><span class="icon material-symbols-outlined" aria-hidden="true">&#xe5cc;</span></a></span>
 </div></nav><div id="latex-macros" class="hidden-content process-math" style="display:none"><span class="process-math">\(\newcommand{\N}{\mathbb N} 
 \newcommand{\Z}{\mathbb Z} 
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@@ -151,6 +151,9 @@ eBookConfig.enable_chatcodes =  false;
 \DeclareMathOperator{\E}{E}
 \DeclareMathOperator{\Var}{Var}
 \DeclareMathOperator{\Cov}{Cov}
+\newcommand{\L}{\mathcal{L}}
+
+\newcommand{\est}{\widehat}
 \newcommand{\lt}{&lt;}
 \newcommand{\gt}{&gt;}
 \newcommand{\amp}{&amp;}
@@ -243,13 +246,17 @@ eBookConfig.enable_chatcodes =  false;
 <li class="toc-item toc-chapter contains-active">
 <div class="toc-title-box"><a href="ch-Confidence-Intervals.html" class="internal"><span class="codenumber">4</span> <span class="title">Confidence Intervals</span></a></div>
 <ul class="structural toc-item-list contains-active">
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Likelihood.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Likelihood</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Likelihood.html#sec-Likelihood-20" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
 <li class="toc-item toc-section contains-active">
-<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Central Limit Theorem</span></a></div>
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+<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Central Limit Theorem</span></a></div>
+<ul class="structural toc-item-list active"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
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 <li class="toc-item toc-section">
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+<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.3</span> <span class="title">Confidence Intervals</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.3</span> <span class="title">Exercises</span></a></div></li></ul>
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+<span class="type">Section</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.2</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Central Limit Theorem</span>
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+<div class="autopermalink" data-description="Exercise 4.2.1"><a href="#exercises-CLT-1" title="Copy heading and permalink for Exercise 4.2.1" aria-label="Copy heading and permalink for Exercise 4.2.1">🔗</a></div></article><article class="exercise exercise-like" id="exercises-CLT-2"><h4 class="heading"><span class="codenumber">2<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
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+<div class="autopermalink" data-description="Exercise 4.2.2"><a href="#exercises-CLT-2" title="Copy heading and permalink for Exercise 4.2.2" aria-label="Copy heading and permalink for Exercise 4.2.2">🔗</a></div></article><article class="exercise exercise-like" id="exercises-CLT-3"><h4 class="heading"><span class="codenumber">3<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
 <div class="introduction" id="exercises-CLT-3-1"><div class="para" id="exercises-CLT-3-1-1">The heights of men in the US have a mean of 69 in and a variance of about 9 in<span class="process-math">\(^2\text{,}\)</span> and the heights of women in the US have a mean of 63.5 in with a variance of 6.25 in<span class="process-math">\(^2\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-CLT-3-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
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 </div>
-<div class="autopermalink" data-description="Task 4.1.3.a"><a href="#exercises-CLT-3-2" title="Copy heading and permalink for Task 4.1.3.a" aria-label="Copy heading and permalink for Task 4.1.3.a">🔗</a></div></article><article class="task exercise-like" id="exercises-CLT-3-3"><h5 class="heading"><span class="codenumber">(b)</span></h5>
+<div class="autopermalink" data-description="Task 4.2.3.a"><a href="#exercises-CLT-3-2" title="Copy heading and permalink for Task 4.2.3.a" aria-label="Copy heading and permalink for Task 4.2.3.a">🔗</a></div></article><article class="task exercise-like" id="exercises-CLT-3-3"><h5 class="heading"><span class="codenumber">(b)</span></h5>
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+<div class="autopermalink" data-description="Task 4.2.3.b"><a href="#exercises-CLT-3-3" title="Copy heading and permalink for Task 4.2.3.b" aria-label="Copy heading and permalink for Task 4.2.3.b">🔗</a></div></article><article class="task exercise-like" id="exercises-CLT-3-4"><h5 class="heading"><span class="codenumber">(c)</span></h5>
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-<div class="autopermalink" data-description="Task 4.1.3.c"><a href="#exercises-CLT-3-4" title="Copy heading and permalink for Task 4.1.3.c" aria-label="Copy heading and permalink for Task 4.1.3.c">🔗</a></div></article><div class="autopermalink" data-description="Exercise 4.1.3"><a href="#exercises-CLT-3" title="Copy heading and permalink for Exercise 4.1.3" aria-label="Copy heading and permalink for Exercise 4.1.3">🔗</a></div></article><div class="autopermalink" data-description="Exercises 4.1"><a href="#exercises-CLT" title="Copy heading and permalink for Exercises 4.1" aria-label="Copy heading and permalink for Exercises 4.1">🔗</a></div></section><div class="autopermalink" data-description="Section 4.1: Central Limit Theorem"><a href="#sec-CLT" title="Copy heading and permalink for Section 4.1: Central Limit Theorem" aria-label="Copy heading and permalink for Section 4.1: Central Limit Theorem">🔗</a></div></section></div>
+<div class="autopermalink" data-description="Task 4.2.3.c"><a href="#exercises-CLT-3-4" title="Copy heading and permalink for Task 4.2.3.c" aria-label="Copy heading and permalink for Task 4.2.3.c">🔗</a></div></article><div class="autopermalink" data-description="Exercise 4.2.3"><a href="#exercises-CLT-3" title="Copy heading and permalink for Exercise 4.2.3" aria-label="Copy heading and permalink for Exercise 4.2.3">🔗</a></div></article><div class="autopermalink" data-description="Exercises 4.2"><a href="#exercises-CLT" title="Copy heading and permalink for Exercises 4.2" aria-label="Copy heading and permalink for Exercises 4.2">🔗</a></div></section><div class="autopermalink" data-description="Section 4.2: Central Limit Theorem"><a href="#sec-CLT" title="Copy heading and permalink for Section 4.2: Central Limit Theorem" aria-label="Copy heading and permalink for Section 4.2: Central Limit Theorem">🔗</a></div></section></div>
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+<a class="previous-button button" href="sec-Likelihood.html" title="Previous"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe5cb;</span><span class="name">Prev</span></a><a class="top-button button" href="#" title="Top"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe5ce;</span><span class="name">Top</span></a><a class="next-button button" href="sec-Confidence-Intervals.html" title="Next"><span class="name">Next</span><span class="icon material-symbols-outlined" aria-hidden="true">&#xe5cc;</span></a>
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sec-Chi-Squared.html

@@ -62,7 +62,7 @@ window.MathJax = {
       "[pretext]/mathjaxknowl3.js"
     ],
     "paths": {
-      "pretext": "_static/pretext/js/lib"
+      "pretext": "_static/pretext/js"
     }
   },
   "startup": {
@@ -79,7 +79,7 @@ window.MathJax = {
 <meta property="og:type" content="book">
 <meta property="book:title" content="Math 1044 Notes">
 <meta property="book:author" content="Andy Eisenberg">
-<script src="_static/pretext/js/lib/jquery.min.js"></script><script src="_static/pretext/js/lib/jquery.sticky.js"></script><script src="_static/pretext/js/lib/jquery.espy.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><script src="_static/pretext/js/user_preferences.js"></script><!--** eBookCongig is necessary to configure interactive       **-->
+<script src="_static/pretext/js/jquery.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><!--** eBookCongig is necessary to configure interactive       **-->
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@@ -101,16 +101,16 @@ eBookConfig.allow_pairs = false;
 eBookConfig.enableScratchAC = false;
 eBookConfig.build_info = "";
 eBookConfig.python3 = null;
-eBookConfig.runestone_version = '7.11.11';
+eBookConfig.runestone_version = '7.11.13';
 eBookConfig.jobehost = '';
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+<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
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+<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
 </script>
 </head>
 <body class="pretext book ignore-math">
@@ -151,6 +151,9 @@ eBookConfig.enable_chatcodes =  false;
 \DeclareMathOperator{\E}{E}
 \DeclareMathOperator{\Var}{Var}
 \DeclareMathOperator{\Cov}{Cov}
+\newcommand{\L}{\mathcal{L}}
+
+\newcommand{\est}{\widehat}
 \newcommand{\lt}{&lt;}
 \newcommand{\gt}{&gt;}
 \newcommand{\amp}{&amp;}
@@ -244,12 +247,16 @@ eBookConfig.enable_chatcodes =  false;
 <div class="toc-title-box"><a href="ch-Confidence-Intervals.html" class="internal"><span class="codenumber">4</span> <span class="title">Confidence Intervals</span></a></div>
 <ul class="structural toc-item-list">
 <li class="toc-item toc-section">
-<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Central Limit Theorem</span></a></div>
-<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
+<div class="toc-title-box"><a href="sec-Likelihood.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Likelihood</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Likelihood.html#sec-Likelihood-20" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
 </li>
 <li class="toc-item toc-section">
-<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Confidence Intervals</span></a></div>
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+<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Central Limit Theorem</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.3</span> <span class="title">Confidence Intervals</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.3</span> <span class="title">Exercises</span></a></div></li></ul>
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sec-Conditional-Probability.html

@@ -62,7 +62,7 @@ window.MathJax = {
       "[pretext]/mathjaxknowl3.js"
     ],
     "paths": {
-      "pretext": "_static/pretext/js/lib"
+      "pretext": "_static/pretext/js"
     }
   },
   "startup": {
@@ -79,7 +79,7 @@ window.MathJax = {
 <meta property="og:type" content="book">
 <meta property="book:title" content="Math 1044 Notes">
 <meta property="book:author" content="Andy Eisenberg">
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+<script src="_static/pretext/js/jquery.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><!--** eBookCongig is necessary to configure interactive       **-->
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 <!--** No external communication:                              **-->
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@@ -101,16 +101,16 @@ eBookConfig.allow_pairs = false;
 eBookConfig.enableScratchAC = false;
 eBookConfig.build_info = "";
 eBookConfig.python3 = null;
-eBookConfig.runestone_version = '7.11.11';
+eBookConfig.runestone_version = '7.11.13';
 eBookConfig.jobehost = '';
 eBookConfig.proxyuri_runs = '';
 eBookConfig.proxyuri_files = '';
 eBookConfig.enable_chatcodes =  false;
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+<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
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+<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
 </script>
 </head>
 <body class="pretext book ignore-math">
@@ -151,6 +151,9 @@ eBookConfig.enable_chatcodes =  false;
 \DeclareMathOperator{\E}{E}
 \DeclareMathOperator{\Var}{Var}
 \DeclareMathOperator{\Cov}{Cov}
+\newcommand{\L}{\mathcal{L}}
+
+\newcommand{\est}{\widehat}
 \newcommand{\lt}{&lt;}
 \newcommand{\gt}{&gt;}
 \newcommand{\amp}{&amp;}
@@ -244,12 +247,16 @@ eBookConfig.enable_chatcodes =  false;
 <div class="toc-title-box"><a href="ch-Confidence-Intervals.html" class="internal"><span class="codenumber">4</span> <span class="title">Confidence Intervals</span></a></div>
 <ul class="structural toc-item-list">
 <li class="toc-item toc-section">
-<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Central Limit Theorem</span></a></div>
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+<div class="toc-title-box"><a href="sec-Likelihood.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Likelihood</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Likelihood.html#sec-Likelihood-20" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
 </li>
 <li class="toc-item toc-section">
-<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Confidence Intervals</span></a></div>
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+<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Central Limit Theorem</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.3</span> <span class="title">Confidence Intervals</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.3</span> <span class="title">Exercises</span></a></div></li></ul>
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sec-Confidence-Intervals.html

@@ -62,7 +62,7 @@ window.MathJax = {
       "[pretext]/mathjaxknowl3.js"
     ],
     "paths": {
-      "pretext": "_static/pretext/js/lib"
+      "pretext": "_static/pretext/js"
     }
   },
   "startup": {
@@ -79,7 +79,7 @@ window.MathJax = {
 <meta property="og:type" content="book">
 <meta property="book:title" content="Math 1044 Notes">
 <meta property="book:author" content="Andy Eisenberg">
-<script src="_static/pretext/js/lib/jquery.min.js"></script><script src="_static/pretext/js/lib/jquery.sticky.js"></script><script src="_static/pretext/js/lib/jquery.espy.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><script src="_static/pretext/js/user_preferences.js"></script><!--** eBookCongig is necessary to configure interactive       **-->
+<script src="_static/pretext/js/jquery.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><!--** eBookCongig is necessary to configure interactive       **-->
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 <!--** No external communication:                              **-->
 <!--**     log level is 0, Runestone Services are disabled     **-->
@@ -101,16 +101,16 @@ eBookConfig.allow_pairs = false;
 eBookConfig.enableScratchAC = false;
 eBookConfig.build_info = "";
 eBookConfig.python3 = null;
-eBookConfig.runestone_version = '7.11.11';
+eBookConfig.runestone_version = '7.11.13';
 eBookConfig.jobehost = '';
 eBookConfig.proxyuri_runs = '';
 eBookConfig.proxyuri_files = '';
 eBookConfig.enable_chatcodes =  false;
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+<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
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+<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
 </script>
 </head>
 <body class="pretext book ignore-math">
@@ -151,6 +151,9 @@ eBookConfig.enable_chatcodes =  false;
 \DeclareMathOperator{\E}{E}
 \DeclareMathOperator{\Var}{Var}
 \DeclareMathOperator{\Cov}{Cov}
+\newcommand{\L}{\mathcal{L}}
+
+\newcommand{\est}{\widehat}
 \newcommand{\lt}{&lt;}
 \newcommand{\gt}{&gt;}
 \newcommand{\amp}{&amp;}
@@ -244,12 +247,16 @@ eBookConfig.enable_chatcodes =  false;
 <div class="toc-title-box"><a href="ch-Confidence-Intervals.html" class="internal"><span class="codenumber">4</span> <span class="title">Confidence Intervals</span></a></div>
 <ul class="structural toc-item-list contains-active">
 <li class="toc-item toc-section">
-<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Central Limit Theorem</span></a></div>
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+<div class="toc-title-box"><a href="sec-Likelihood.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Likelihood</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Likelihood.html#sec-Likelihood-20" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Central Limit Theorem</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
 </li>
 <li class="toc-item toc-section contains-active">
-<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Confidence Intervals</span></a></div>
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+<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.3</span> <span class="title">Confidence Intervals</span></a></div>
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 <main class="ptx-main"><div id="ptx-content" class="ptx-content"><section class="section" id="sec-Confidence-Intervals"><h2 class="heading hide-type">
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+<span class="type">Section</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.3</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Confidence Intervals</span>
 </h2>
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 </div>
@@ -300,18 +307,18 @@ eBookConfig.enable_chatcodes =  false;
 <article class="exercise exercise-like" id="exercises-Confidence-Intervals-1"><h4 class="heading"><span class="codenumber">1<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
 <div class="para" id="exercises-Confidence-Intervals-1-1-1">Suppose we flip a coin 100 times and count 60 heads. Let <span class="process-math">\(p\)</span> be the (unknown) probability that the coin comes up heads on a flip. Give an approximate 95% confidence interval for the value of <span class="process-math">\(p\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-Confidence-Intervals-1-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
 </div>
-<div class="autopermalink" data-description="Exercise 4.2.1"><a href="#exercises-Confidence-Intervals-1" title="Copy heading and permalink for Exercise 4.2.1" aria-label="Copy heading and permalink for Exercise 4.2.1">🔗</a></div></article><article class="exercise exercise-like" id="exercises-Confidence-Intervals-2"><h4 class="heading"><span class="codenumber">2<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
+<div class="autopermalink" data-description="Exercise 4.3.1"><a href="#exercises-Confidence-Intervals-1" title="Copy heading and permalink for Exercise 4.3.1" aria-label="Copy heading and permalink for Exercise 4.3.1">🔗</a></div></article><article class="exercise exercise-like" id="exercises-Confidence-Intervals-2"><h4 class="heading"><span class="codenumber">2<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
 <div class="introduction" id="exercises-Confidence-Intervals-2-1"><div class="para" id="exercises-Confidence-Intervals-2-1-1">Suppose in a sample of 100 people, 12 are left-handed.<div class="autopermalink" data-description="Paragraph"><a href="#exercises-Confidence-Intervals-2-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
 </div></div>
 <article class="task exercise-like" id="exercises-Confidence-Intervals-2-2"><h5 class="heading"><span class="codenumber">(a)</span></h5>
 <div class="para" id="exercises-Confidence-Intervals-2-2-1-1">Give a 95% confidence interval for the proportion <span class="process-math">\(p\)</span> of left-handed people.<div class="autopermalink" data-description="Paragraph"><a href="#exercises-Confidence-Intervals-2-2-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
 </div>
-<div class="autopermalink" data-description="Task 4.2.2.a"><a href="#exercises-Confidence-Intervals-2-2" title="Copy heading and permalink for Task 4.2.2.a" aria-label="Copy heading and permalink for Task 4.2.2.a">🔗</a></div></article><article class="task exercise-like" id="exercises-Confidence-Intervals-2-3"><h5 class="heading"><span class="codenumber">(b)</span></h5>
+<div class="autopermalink" data-description="Task 4.3.2.a"><a href="#exercises-Confidence-Intervals-2-2" title="Copy heading and permalink for Task 4.3.2.a" aria-label="Copy heading and permalink for Task 4.3.2.a">🔗</a></div></article><article class="task exercise-like" id="exercises-Confidence-Intervals-2-3"><h5 class="heading"><span class="codenumber">(b)</span></h5>
 <div class="para" id="exercises-Confidence-Intervals-2-3-1-1">Give a 90% confidence interval.<div class="autopermalink" data-description="Paragraph"><a href="#exercises-Confidence-Intervals-2-3-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
 </div>
-<div class="autopermalink" data-description="Task 4.2.2.b"><a href="#exercises-Confidence-Intervals-2-3" title="Copy heading and permalink for Task 4.2.2.b" aria-label="Copy heading and permalink for Task 4.2.2.b">🔗</a></div></article><div class="autopermalink" data-description="Exercise 4.2.2"><a href="#exercises-Confidence-Intervals-2" title="Copy heading and permalink for Exercise 4.2.2" aria-label="Copy heading and permalink for Exercise 4.2.2">🔗</a></div></article><article class="exercise exercise-like" id="exercises-Confidence-Intervals-3"><h4 class="heading"><span class="codenumber">3<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
+<div class="autopermalink" data-description="Task 4.3.2.b"><a href="#exercises-Confidence-Intervals-2-3" title="Copy heading and permalink for Task 4.3.2.b" aria-label="Copy heading and permalink for Task 4.3.2.b">🔗</a></div></article><div class="autopermalink" data-description="Exercise 4.3.2"><a href="#exercises-Confidence-Intervals-2" title="Copy heading and permalink for Exercise 4.3.2" aria-label="Copy heading and permalink for Exercise 4.3.2">🔗</a></div></article><article class="exercise exercise-like" id="exercises-Confidence-Intervals-3"><h4 class="heading"><span class="codenumber">3<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
 <div class="para" id="exercises-Confidence-Intervals-3-1-1">The weights of five mice are measured and recorded below. Give a 95% confidence interval for the sample mean weight of mice. (Pretend 5 measurements is large enough for the CLT to apply.)<div class="autopermalink" data-description="Paragraph"><a href="#exercises-Confidence-Intervals-3-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
-</div> <figure class="table table-like" id="exercises-Confidence-Intervals-3-1-2"><figcaption><span class="type">Table</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.2.1<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span><div class="autopermalink" data-description="Table 4.2.1: "><a href="#exercises-Confidence-Intervals-3-1-2" title="Copy heading and permalink for Table 4.2.1: " aria-label="Copy heading and permalink for Table 4.2.1: ">🔗</a></div></figcaption><div class="tabular-box natural-width"><table class="tabular">
+</div> <figure class="table table-like" id="exercises-Confidence-Intervals-3-1-2"><figcaption><span class="type">Table</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.3.1<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span><div class="autopermalink" data-description="Table 4.3.1: "><a href="#exercises-Confidence-Intervals-3-1-2" title="Copy heading and permalink for Table 4.3.1: " aria-label="Copy heading and permalink for Table 4.3.1: ">🔗</a></div></figcaption><div class="tabular-box natural-width"><table class="tabular">
 <tr class="header-horizontal">
 <th scope="col" class="c m b0 r0 l0 t0 lines">mouse <span class="process-math">\(i\)</span>
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@@ -329,9 +336,9 @@ eBookConfig.enable_chatcodes =  false;
 <td class="c m b0 r0 l0 t0 lines">20</td>
 <td class="c m b0 r0 l0 t0 lines">29</td>
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-</table></div></figure><div class="autopermalink" data-description="Exercise 4.2.3"><a href="#exercises-Confidence-Intervals-3" title="Copy heading and permalink for Exercise 4.2.3" aria-label="Copy heading and permalink for Exercise 4.2.3">🔗</a></div></article><article class="exercise exercise-like" id="exercises-Confidence-Intervals-4"><h4 class="heading"><span class="codenumber">4<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
+</table></div></figure><div class="autopermalink" data-description="Exercise 4.3.3"><a href="#exercises-Confidence-Intervals-3" title="Copy heading and permalink for Exercise 4.3.3" aria-label="Copy heading and permalink for Exercise 4.3.3">🔗</a></div></article><article class="exercise exercise-like" id="exercises-Confidence-Intervals-4"><h4 class="heading"><span class="codenumber">4<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
 <div class="para" id="exercises-Confidence-Intervals-4-1-1">The heights of five plants are measured and recorded below. Give a 95% confidence interval around the sample mean for the heights of the plants. (Pretend 5 measurements is large enough for the CLT to apply.)<div class="autopermalink" data-description="Paragraph"><a href="#exercises-Confidence-Intervals-4-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
-</div> <figure class="table table-like" id="exercises-Confidence-Intervals-4-1-2"><figcaption><span class="type">Table</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.2.2<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span><div class="autopermalink" data-description="Table 4.2.2: "><a href="#exercises-Confidence-Intervals-4-1-2" title="Copy heading and permalink for Table 4.2.2: " aria-label="Copy heading and permalink for Table 4.2.2: ">🔗</a></div></figcaption><div class="tabular-box natural-width"><table class="tabular">
+</div> <figure class="table table-like" id="exercises-Confidence-Intervals-4-1-2"><figcaption><span class="type">Table</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.3.2<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span><div class="autopermalink" data-description="Table 4.3.2: "><a href="#exercises-Confidence-Intervals-4-1-2" title="Copy heading and permalink for Table 4.3.2: " aria-label="Copy heading and permalink for Table 4.3.2: ">🔗</a></div></figcaption><div class="tabular-box natural-width"><table class="tabular">
 <tr class="header-horizontal">
 <th scope="col" class="c m b0 r0 l0 t0 lines">plant <span class="process-math">\(i\)</span>
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@@ -349,7 +356,7 @@ eBookConfig.enable_chatcodes =  false;
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 </tr>
-</table></div></figure><div class="autopermalink" data-description="Exercise 4.2.4"><a href="#exercises-Confidence-Intervals-4" title="Copy heading and permalink for Exercise 4.2.4" aria-label="Copy heading and permalink for Exercise 4.2.4">🔗</a></div></article><div class="autopermalink" data-description="Exercises 4.2"><a href="#exercises-Confidence-Intervals" title="Copy heading and permalink for Exercises 4.2" aria-label="Copy heading and permalink for Exercises 4.2">🔗</a></div></section><div class="autopermalink" data-description="Section 4.2: Confidence Intervals"><a href="#sec-Confidence-Intervals" title="Copy heading and permalink for Section 4.2: Confidence Intervals" aria-label="Copy heading and permalink for Section 4.2: Confidence Intervals">🔗</a></div></section></div>
+</table></div></figure><div class="autopermalink" data-description="Exercise 4.3.4"><a href="#exercises-Confidence-Intervals-4" title="Copy heading and permalink for Exercise 4.3.4" aria-label="Copy heading and permalink for Exercise 4.3.4">🔗</a></div></article><div class="autopermalink" data-description="Exercises 4.3"><a href="#exercises-Confidence-Intervals" title="Copy heading and permalink for Exercises 4.3" aria-label="Copy heading and permalink for Exercises 4.3">🔗</a></div></section><div class="autopermalink" data-description="Section 4.3: Confidence Intervals"><a href="#sec-Confidence-Intervals" title="Copy heading and permalink for Section 4.3: Confidence Intervals" aria-label="Copy heading and permalink for Section 4.3: Confidence Intervals">🔗</a></div></section></div>
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sec-Continuous-RVs.html

@@ -62,7 +62,7 @@ window.MathJax = {
       "[pretext]/mathjaxknowl3.js"
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 <meta property="og:type" content="book">
 <meta property="book:title" content="Math 1044 Notes">
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+<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
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 <body class="pretext book ignore-math">
@@ -151,6 +151,9 @@ eBookConfig.enable_chatcodes =  false;
 \DeclareMathOperator{\E}{E}
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+\newcommand{\L}{\mathcal{L}}
+
+\newcommand{\est}{\widehat}
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@@ -244,12 +247,16 @@ eBookConfig.enable_chatcodes =  false;
 <div class="toc-title-box"><a href="ch-Confidence-Intervals.html" class="internal"><span class="codenumber">4</span> <span class="title">Confidence Intervals</span></a></div>
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+<div class="toc-title-box"><a href="sec-Likelihood.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Likelihood</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Likelihood.html#sec-Likelihood-20" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
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+<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Central Limit Theorem</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.3</span> <span class="title">Confidence Intervals</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.3</span> <span class="title">Exercises</span></a></div></li></ul>
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sec-Correlation.html

@@ -62,7 +62,7 @@ window.MathJax = {
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+      "pretext": "_static/pretext/js"
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@@ -79,7 +79,7 @@ window.MathJax = {
 <meta property="og:type" content="book">
 <meta property="book:title" content="Math 1044 Notes">
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+\newcommand{\L}{\mathcal{L}}
+
+\newcommand{\est}{\widehat}
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@@ -244,12 +247,16 @@ eBookConfig.enable_chatcodes =  false;
 <div class="toc-title-box"><a href="ch-Confidence-Intervals.html" class="internal"><span class="codenumber">4</span> <span class="title">Confidence Intervals</span></a></div>
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+<div class="toc-title-box"><a href="sec-Likelihood.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Likelihood</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Likelihood.html#sec-Likelihood-20" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
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+<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Central Limit Theorem</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.3</span> <span class="title">Confidence Intervals</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.3</span> <span class="title">Exercises</span></a></div></li></ul>
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sec-Covariance.html

@@ -62,7 +62,7 @@ window.MathJax = {
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+      "pretext": "_static/pretext/js"
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@@ -79,7 +79,7 @@ window.MathJax = {
 <meta property="og:type" content="book">
 <meta property="book:title" content="Math 1044 Notes">
 <meta property="book:author" content="Andy Eisenberg">
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@@ -151,6 +151,9 @@ eBookConfig.enable_chatcodes =  false;
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+\newcommand{\L}{\mathcal{L}}
+
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+<div class="toc-title-box"><a href="sec-Likelihood.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Likelihood</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Likelihood.html#sec-Likelihood-20" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
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+<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Central Limit Theorem</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.3</span> <span class="title">Confidence Intervals</span></a></div>
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@@ -62,7 +62,7 @@ window.MathJax = {
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+      "pretext": "_static/pretext/js"
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-eBookConfig.runestone_version = '7.11.11';
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+<li class="toc-item toc-chapter">
+<div class="toc-title-box"><a href="ch-Introduction.html" class="internal"><span class="codenumber">0</span> <span class="title">Introduction</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-section"><div class="toc-title-box"><a href="sec-Introduction.html" class="internal"><span class="codenumber">0.1</span> <span class="title">Introduction</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-chapter">
+<div class="toc-title-box"><a href="ch-Probability.html" class="internal"><span class="codenumber">1</span> <span class="title">Probability Theory</span></a></div>
+<ul class="structural toc-item-list">
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Set-Theory.html" class="internal"><span class="codenumber">1.1</span> <span class="title">Set Theory</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Set-Theory.html#exercises-Set-Theory" class="internal"><span class="codenumber">1.1</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Probability.html" class="internal"><span class="codenumber">1.2</span> <span class="title">Definition of Probability</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Probability.html#exercises-Probability" class="internal"><span class="codenumber">1.2</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Conditional-Probability.html" class="internal"><span class="codenumber">1.3</span> <span class="title">Conditional Probability</span></a></div>
+<ul class="structural toc-item-list">
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Conditional-Probability.html#subsec-conditional-probability" class="internal"><span class="codenumber">1.3.1</span> <span class="title">Conditional Probability</span></a></div></li>
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Conditional-Probability.html#subsec-diagnostic-testing" class="internal"><span class="codenumber">1.3.2</span> <span class="title">Diagnostic Testing</span></a></div></li>
+<li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Conditional-Probability.html#exercises-Conditional-Probability" class="internal"><span class="codenumber">1.3.3</span> <span class="title">Exercises</span></a></div></li>
+</ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Independent-Events.html" class="internal"><span class="codenumber">1.4</span> <span class="title">Independent Events</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Independent-Events.html#exercises-Independent-Events" class="internal"><span class="codenumber">1.4</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+</ul>
+</li>
+<li class="toc-item toc-chapter">
+<div class="toc-title-box"><a href="ch-Random-Variables.html" class="internal"><span class="codenumber">2</span> <span class="title">Random Variables</span></a></div>
+<ul class="structural toc-item-list">
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Discrete-RVs.html" class="internal"><span class="codenumber">2.1</span> <span class="title">Discrete Random Variables</span></a></div>
+<ul class="structural toc-item-list">
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Discrete-RVs.html#subsec-Discrete-RVs" class="internal"><span class="codenumber">2.1.1</span> <span class="title">Discrete Random Variables</span></a></div></li>
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Discrete-RVs.html#subsec-binomial-distribution" class="internal"><span class="codenumber">2.1.2</span> <span class="title">The Binomial Distribution</span></a></div></li>
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Discrete-RVs.html#subsec-geometric-distribution" class="internal"><span class="codenumber">2.1.3</span> <span class="title">Geometric Distribution</span></a></div></li>
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Discrete-RVs.html#subsec-poisson-distribution" class="internal"><span class="codenumber">2.1.4</span> <span class="title">Poisson Distribution</span></a></div></li>
+<li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Discrete-RVs.html#exercises-Discrete-RVs" class="internal"><span class="codenumber">2.1.5</span> <span class="title">Exercises</span></a></div></li>
+</ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Continuous-RVs.html" class="internal"><span class="codenumber">2.2</span> <span class="title">Continuous Random Variables</span></a></div>
+<ul class="structural toc-item-list">
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Continuous-RVs.html#subsec-pdfs" class="internal"><span class="codenumber">2.2.1</span> <span class="title">Probability Density Functions</span></a></div></li>
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Continuous-RVs.html#subsec-cdf" class="internal"><span class="codenumber">2.2.2</span> <span class="title">Cumulative Distribution Functions</span></a></div></li>
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Continuous-RVs.html#subsec-exponential-distribution" class="internal"><span class="codenumber">2.2.3</span> <span class="title">The Exponential Distribution</span></a></div></li>
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Continuous-RVs.html#subsec-normal-distribution" class="internal"><span class="codenumber">2.2.4</span> <span class="title">Normal Distribution</span></a></div></li>
+<li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Continuous-RVs.html#exercises-Continuous-RVs" class="internal"><span class="codenumber">2.2.5</span> <span class="title">Exercises</span></a></div></li>
+</ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Joint-Distributions.html" class="internal"><span class="codenumber">2.3</span> <span class="title">Joint Distributions</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Joint-Distributions.html#exercises-Joint-Distributions" class="internal"><span class="codenumber">2.3</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+</ul>
+</li>
+<li class="toc-item toc-chapter">
+<div class="toc-title-box"><a href="ch-Expected-Value.html" class="internal"><span class="codenumber">3</span> <span class="title">Expected Value and Variance</span></a></div>
+<ul class="structural toc-item-list">
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Expected-Value.html" class="internal"><span class="codenumber">3.1</span> <span class="title">Expected Value</span></a></div>
+<ul class="structural toc-item-list">
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Expected-Value.html#subsec-discrete-EV" class="internal"><span class="codenumber">3.1.1</span> <span class="title">Discrete Expected Value</span></a></div></li>
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Expected-Value.html#subsec-continuous-EV" class="internal"><span class="codenumber">3.1.2</span> <span class="title">Continuous Expected Value</span></a></div></li>
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Expected-Value.html#subsec-linearity-EV" class="internal"><span class="codenumber">3.1.3</span> <span class="title">Linearity of Expected Value</span></a></div></li>
+<li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Expected-Value.html#exercises-Expected-Value" class="internal"><span class="codenumber">3.1.4</span> <span class="title">Exercises</span></a></div></li>
+</ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Variance.html" class="internal"><span class="codenumber">3.2</span> <span class="title">Variance</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Variance.html#exercises-Variance" class="internal"><span class="codenumber">3.2</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Covariance.html" class="internal"><span class="codenumber">3.3</span> <span class="title">Covariance</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Covariance.html#exercises-Covariance" class="internal"><span class="codenumber">3.3</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+</ul>
+</li>
+<li class="toc-item toc-chapter contains-active">
+<div class="toc-title-box"><a href="ch-Confidence-Intervals.html" class="internal"><span class="codenumber">4</span> <span class="title">Confidence Intervals</span></a></div>
+<ul class="structural toc-item-list contains-active">
+<li class="toc-item toc-section"><div class="toc-title-box"><a href="sec-Likelihood.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Likelihood</span></a></div></li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Central Limit Theorem</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.3</span> <span class="title">Confidence Intervals</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.3</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section contains-active">
+<div class="toc-title-box"><a href="sec-Example.html" class="internal"><span class="codenumber">4.4</span> <span class="title">Example</span></a></div>
+<ul class="structural toc-item-list active"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Example.html#sec-Example-8" class="internal"><span class="codenumber">4.4</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+</ul>
+</li>
+<li class="toc-item toc-chapter">
+<div class="toc-title-box"><a href="ch-Hypothesis-Testing.html" class="internal"><span class="codenumber">5</span> <span class="title">Hypothesis Testing</span></a></div>
+<ul class="structural toc-item-list">
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-One-Sample-Tests.html" class="internal"><span class="codenumber">5.1</span> <span class="title">One Sample Tests</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-One-Sample-Tests.html#exercises-One-Sample-Tests" class="internal"><span class="codenumber">5.1</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Two-Sample-Tests.html" class="internal"><span class="codenumber">5.2</span> <span class="title">Two Sample Tests</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Two-Sample-Tests.html#exercises-Two-Sample-Tests" class="internal"><span class="codenumber">5.2</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Power.html" class="internal"><span class="codenumber">5.3</span> <span class="title">Power of a Test</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Power.html#exercises-Power" class="internal"><span class="codenumber">5.3</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Chi-Squared.html" class="internal"><span class="codenumber">5.4</span> <span class="title"><span class="process-math">\(\chi^2\)</span> Test</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Chi-Squared.html#exercises-Chi-Squared" class="internal"><span class="codenumber">5.4</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+</ul>
+</li>
+<li class="toc-item toc-chapter">
+<div class="toc-title-box"><a href="ch-Linear-Regression.html" class="internal"><span class="codenumber">6</span> <span class="title">Linear Regression</span></a></div>
+<ul class="structural toc-item-list">
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Correlation.html" class="internal"><span class="codenumber">6.1</span> <span class="title">Correlation</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Correlation.html#exercises-Correlation" class="internal"><span class="codenumber">6.1</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Linear-Regression.html" class="internal"><span class="codenumber">6.2</span> <span class="title">Linear Regression</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Linear-Regression.html#exercises-Linear-Regression" class="internal"><span class="codenumber">6.2</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+</ul>
+</li>
+<li class="toc-item toc-backmatter"><div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div></li>
+</ul></nav></div>
+<main class="ptx-main"><div id="ptx-content" class="ptx-content"><section class="section" id="sec-Example"><h2 class="heading hide-type">
+<span class="type">Section</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.4</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Example</span>
+</h2>
+<div class="para" id="sec-Example-2">Welcome to PreTeXt. Let’s type up some math. According to Pythagoras, <span class="process-math">\(a^2 + b^2 = c^2\text{.}\)</span> But he also thought <span class="process-math">\(\sqrt{2}\)</span> was rational, so maybe we shouldn’t take his word for it. Let’s see a proof by picture.<div class="autopermalink" data-description="Paragraph"><a href="#sec-Example-2" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<article class="theorem theorem-like" id="thm-Pythagorean-Theorem"><h3 class="heading">
+<span class="type">Theorem</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.4.1</span><span class="period heading-divison-mark heading-divison-mark__period">.</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Pythagorean Theorem.</span>
+</h3>
+<div class="para logical" id="thm-Pythagorean-Theorem-2-1">
+<div class="para">Suppose a triangle has side lengths <span class="process-math">\(a, b\)</span> and hypotenuse length <span class="process-math">\(c\text{.}\)</span> Then</div>
+<div class="displaymath process-math" id="thm-Pythagorean-Theorem-2-1-3">
+\begin{gather*}
+a^2 + b^2 = c^2. 
+\end{gather*}
+</div>
+<div class="autopermalink" data-description="Paragraph"><a href="#thm-Pythagorean-Theorem-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Theorem 4.4.1: Pythagorean Theorem"><a href="#thm-Pythagorean-Theorem" title="Copy heading and permalink for Theorem 4.4.1: Pythagorean Theorem" aria-label="Copy heading and permalink for Theorem 4.4.1: Pythagorean Theorem">🔗</a></div></article><details id="thm-Pythagorean-Theorem-3" class="hiddenproof born-hidden-knowl"><summary class="knowl__link"><h3 class="heading"><span class="type">Proof<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h3></summary><article class="hiddenproof knowl__content"><div class="image-box" style="width: 50%; margin-left: 25%; margin-right: 25%;">
+<img src="external/./example.png" class="contained" alt="Right triangle with squares appended to each side."><details class="image-description" aria-live="polite"><summary title="details"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe88e;</span></summary><div id="thm-Pythagorean-Theorem-3-1-description"><div class="para" id="thm-Pythagorean-Theorem-3-1-2-1">Right triangle with legs labeled <span class="process-math">\(a\)</span> and <span class="process-math">\(b\)</span> and hypotenuse labeled <span class="process-math">\(c\text{.}\)</span> Squares are appended to each side of the triangle.<div class="autopermalink" data-description="Paragraph"><a href="#thm-Pythagorean-Theorem-3-1-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div></div></details>
+</div>
+<div class="autopermalink" data-description="Proof 4.4.1.1"><a href="#thm-Pythagorean-Theorem-3" title="Copy heading and permalink for Proof 4.4.1.1" aria-label="Copy heading and permalink for Proof 4.4.1.1">🔗</a></div></article></details><article class="definition definition-like" id="def-rational"><h3 class="heading">
+<span class="type">Definition</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.4.2</span><span class="period heading-divison-mark heading-divison-mark__period">.</span>
+</h3>
+<div class="para" id="def-rational-1-1">A real number <span class="process-math">\(x \in \R\)</span> is called <dfn class="terminology">rational</dfn> if there are integers <span class="process-math">\(a, b\)</span> so that <span class="process-math">\(x = \frac{a}{b}\text{.}\)</span> Otherwise, <span class="process-math">\(x\)</span> is called <dfn class="terminology">irrational</dfn>, no matter what Pythagoras says.<div class="autopermalink" data-description="Paragraph"><a href="#def-rational-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Definition 4.4.2"><a href="#def-rational" title="Copy heading and permalink for Definition 4.4.2" aria-label="Copy heading and permalink for Definition 4.4.2">🔗</a></div></article><article class="example example-like" id="sec-Example-5"><h3 class="heading">
+<span class="type">Example</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.4.3</span><span class="period heading-divison-mark heading-divison-mark__period">.</span>
+</h3>
+<div class="para" id="sec-Example-5-1">
+<span class="process-math">\(\frac{1}{2}\)</span> is rational.<div class="autopermalink" data-description="Paragraph"><a href="#sec-Example-5-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Example 4.4.3"><a href="#sec-Example-5" title="Copy heading and permalink for Example 4.4.3" aria-label="Copy heading and permalink for Example 4.4.3">🔗</a></div></article><article class="example example-like" id="sec-Example-6"><h3 class="heading">
+<span class="type">Example</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.4.4</span><span class="period heading-divison-mark heading-divison-mark__period">.</span>
+</h3>
+<div class="para" id="sec-Example-6-1-1">Is <span class="process-math">\(\sqrt{2}\)</span> rational?<div class="autopermalink" data-description="Paragraph"><a href="#sec-Example-6-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="solutions">
+<details id="sec-Example-6-2" class="hint solution-like born-hidden-knowl"><summary class="knowl__link"><span class="type">Hint</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">1</span><span class="period heading-divison-mark heading-divison-mark__period">.</span></summary><div class="hint solution-like knowl__content">
+<div class="para" id="sec-Example-6-2-1">Why does <span class="process-math">\(\pi = \frac{\sqrt{2}}{1}\)</span> <em class="emphasis">not</em> show that <span class="process-math">\(\sqrt{2}\)</span> is rational?<div class="autopermalink" data-description="Paragraph"><a href="#sec-Example-6-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Hint 4.4.4.1"><a href="#sec-Example-6-2" title="Copy heading and permalink for Hint 4.4.4.1" aria-label="Copy heading and permalink for Hint 4.4.4.1">🔗</a></div>
+</div></details><details id="sec-Example-6-3" class="hint solution-like born-hidden-knowl"><summary class="knowl__link"><span class="type">Hint</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">2</span><span class="period heading-divison-mark heading-divison-mark__period">.</span></summary><div class="hint solution-like knowl__content">
+<div class="para" id="sec-Example-6-3-1">What would happen if you assumed <span class="process-math">\(\sqrt{2}\)</span> is rational?<div class="autopermalink" data-description="Paragraph"><a href="#sec-Example-6-3-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Hint 4.4.4.2"><a href="#sec-Example-6-3" title="Copy heading and permalink for Hint 4.4.4.2" aria-label="Copy heading and permalink for Hint 4.4.4.2">🔗</a></div>
+</div></details><details id="sec-Example-6-4" class="answer solution-like born-hidden-knowl"><summary class="knowl__link"><span class="type">Answer</span><span class="period heading-divison-mark heading-divison-mark__period">.</span></summary><div class="answer solution-like knowl__content">
+<div class="para" id="sec-Example-6-4-1">No!<div class="autopermalink" data-description="Paragraph"><a href="#sec-Example-6-4-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Answer 4.4.4.1"><a href="#sec-Example-6-4" title="Copy heading and permalink for Answer 4.4.4.1" aria-label="Copy heading and permalink for Answer 4.4.4.1">🔗</a></div>
+</div></details><details id="sec-Example-6-5" class="solution solution-like born-hidden-knowl"><summary class="knowl__link"><span class="type">Solution</span><span class="period heading-divison-mark heading-divison-mark__period">.</span></summary><div class="solution solution-like knowl__content">
+<div class="para logical" id="sec-Example-6-5-1">
+<div class="para">Suppose that <span class="process-math">\(\sqrt{2} = \frac{a}{b}\)</span> for relatively prime integers <span class="process-math">\(a, b\text{.}\)</span> Then:</div>
+<div class="displaymath process-math" id="sec-Example-6-5-1-3">
+\begin{align*}
+2 \amp = \frac{a^2}{b^2}\\
+2b^2 \amp = a^2
+\end{align*}
+</div>
+<div class="para">But, after taking the prime factorization of both sides, the left side has an odd number of prime factors and the right side has an even number. This is a contradiction, so <span class="process-math">\(\sqrt{2}\)</span> is irrational.</div>
+<div class="autopermalink" data-description="Paragraph"><a href="#sec-Example-6-5-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Solution 4.4.4.1"><a href="#sec-Example-6-5" title="Copy heading and permalink for Solution 4.4.4.1" aria-label="Copy heading and permalink for Solution 4.4.4.1">🔗</a></div>
+</div></details>
+</div>
+<div class="autopermalink" data-description="Example 4.4.4"><a href="#sec-Example-6" title="Copy heading and permalink for Example 4.4.4" aria-label="Copy heading and permalink for Example 4.4.4">🔗</a></div></article><details id="sec-Example-7" class="exercise exercise-like born-hidden-knowl"><summary class="knowl__link"><h3 class="heading">
+<span class="type">Exercise</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.4.5</span><span class="period heading-divison-mark heading-divison-mark__period">.</span>
+</h3></summary><article class="exercise exercise-like knowl__content"><div class="para" id="sec-Example-7-1-1">Prove that <span class="process-math">\(\sqrt{3}\)</span> is irrational.<div class="autopermalink" data-description="Paragraph"><a href="#sec-Example-7-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Exercise 4.4.5"><a href="#sec-Example-7" title="Copy heading and permalink for Exercise 4.4.5" aria-label="Copy heading and permalink for Exercise 4.4.5">🔗</a></div></article></details><section class="exercises" id="sec-Example-8"><h3 class="heading hide-type">
+<span class="type">Exercises</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber"></span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Exercises</span>
+</h3>
+<article class="exercise exercise-like" id="sec-Example-8-1"><h4 class="heading"><span class="codenumber">1<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
+<div class="para" id="sec-Example-8-1-1">An exercise.<div class="autopermalink" data-description="Paragraph"><a href="#sec-Example-8-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Exercise 4.4.1"><a href="#sec-Example-8-1" title="Copy heading and permalink for Exercise 4.4.1" aria-label="Copy heading and permalink for Exercise 4.4.1">🔗</a></div></article><article class="exercise exercise-like" id="sec-Example-8-2"><h4 class="heading"><span class="codenumber">2<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
+<div class="para" id="sec-Example-8-2-1">An exercise.<div class="autopermalink" data-description="Paragraph"><a href="#sec-Example-8-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Exercise 4.4.2"><a href="#sec-Example-8-2" title="Copy heading and permalink for Exercise 4.4.2" aria-label="Copy heading and permalink for Exercise 4.4.2">🔗</a></div></article><article class="exercise exercise-like" id="sec-Example-8-3"><h4 class="heading"><span class="codenumber">3<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
+<div class="para" id="sec-Example-8-3-1">An exercise.<div class="autopermalink" data-description="Paragraph"><a href="#sec-Example-8-3-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Exercise 4.4.3"><a href="#sec-Example-8-3" title="Copy heading and permalink for Exercise 4.4.3" aria-label="Copy heading and permalink for Exercise 4.4.3">🔗</a></div></article><article class="exercise exercise-like" id="sec-Example-8-4"><h4 class="heading"><span class="codenumber">4<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
+<div class="para" id="sec-Example-8-4-1">An exercise.<div class="autopermalink" data-description="Paragraph"><a href="#sec-Example-8-4-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Exercise 4.4.4"><a href="#sec-Example-8-4" title="Copy heading and permalink for Exercise 4.4.4" aria-label="Copy heading and permalink for Exercise 4.4.4">🔗</a></div></article><div class="autopermalink" data-description="Exercises 4.4"><a href="#sec-Example-8" title="Copy heading and permalink for Exercises 4.4" aria-label="Copy heading and permalink for Exercises 4.4">🔗</a></div></section><div class="autopermalink" data-description="Section 4.4: Example"><a href="#sec-Example" title="Copy heading and permalink for Section 4.4: Example" aria-label="Copy heading and permalink for Section 4.4: Example">🔗</a></div></section></div>
+<div id="ptx-content-footer" class="ptx-content-footer">
+<a class="previous-button button" href="sec-Confidence-Intervals.html" title="Previous"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe5cb;</span><span class="name">Prev</span></a><a class="top-button button" href="#" title="Top"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe5ce;</span><span class="name">Top</span></a><a class="next-button button" href="ch-Hypothesis-Testing.html" title="Next"><span class="name">Next</span><span class="icon material-symbols-outlined" aria-hidden="true">&#xe5cc;</span></a>
+</div></main>
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+<div id="ptx-page-footer" class="ptx-page-footer">
+<a class="pretext-link" href="https://pretextbook.org" title="PreTeXt"><div class="logo"><svg xmlns="http://www.w3.org/2000/svg" height="100%" viewBox="338 3000 8772 6866" role="img"><title>PreTeXt logo</title><g style="stroke-width:.025in; stroke:currentColor; fill:none"><polyline points="472,3590 472,9732 " style="stroke-width:174; stroke-linejoin:miter; stroke-linecap:round; "></polyline><path style="stroke-width:126;stroke-linecap:butt;" d="M 4724,9448 A 4660 4660  0  0  1  8598  9259"></path><path style="stroke-width:174;stroke-linecap:butt;" d="M 4488,9685 A 4228 4228  0  0  0   472  9732"></path><path style="stroke-width:126;stroke-linecap:butt;" d="M 4724,3590 A 4241 4241  0  0  1  8598  3496"></path><path style="stroke-width:126;stroke-linecap:round;" d="M 850,3496  A 4241 4241  0  0  1  4724  3590"></path><path style="stroke-width:126;stroke-linecap:round;" d="M 850,9259  A 4507 4507  0  0  1  4724  9448"></path><polyline points="5385,4299 4062,8125" style="stroke-width:300; stroke-linejoin:miter; stroke-linecap:round;"></polyline><polyline points="8598,3496 8598,9259" style="stroke-width:126; stroke-linejoin:miter; stroke-linecap:round;"></polyline><polyline points="850,3496 850,9259" style="stroke-width:126; stroke-linejoin:miter; stroke-linecap:round;"></polyline><polyline points="4960,9685 4488,9685" style="stroke-width:174; stroke-linejoin:miter; stroke-linecap:round;"></polyline><polyline points="3070,4582 1889,6141 3070,7700" style="stroke-width:300; stroke-linejoin:miter; stroke-linecap:round;"></polyline><polyline points="6418,4582 7600,6141 6418,7700" style="stroke-width:300; stroke-linejoin:miter; stroke-linecap:round;"></polyline><polyline points="8976,3590 8976,9732" style="stroke-width:174; stroke-linejoin:miter; stroke-linecap:round;"></polyline><path style="stroke-width:174;stroke-linecap:butt;" d="M 4960,9685 A 4228 4228  0  0  1  8976  9732"></path></g></svg></div></a><a class="runestone-link" href="https://runestone.academy" title="Runestone Academy"><img class="logo" src="https://runestone.academy/runestone/static/images/RAIcon_cropped.png" alt="Runstone Academy logo"></a><a class="mathjax-link" href="https://www.mathjax.org" title="MathJax"><img class="logo" src="https://www.mathjax.org/badge/badge-square-2.png" alt="MathJax logo"></a>
+</div>
+</body>
+</html>

sec-Expected-Value.html

@@ -62,7 +62,7 @@ window.MathJax = {
       "[pretext]/mathjaxknowl3.js"
     ],
     "paths": {
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+      "pretext": "_static/pretext/js"
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+<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
 </script>
 </head>
 <body class="pretext book ignore-math">
@@ -151,6 +151,9 @@ eBookConfig.enable_chatcodes =  false;
 \DeclareMathOperator{\E}{E}
 \DeclareMathOperator{\Var}{Var}
 \DeclareMathOperator{\Cov}{Cov}
+\newcommand{\L}{\mathcal{L}}
+
+\newcommand{\est}{\widehat}
 \newcommand{\lt}{&lt;}
 \newcommand{\gt}{&gt;}
 \newcommand{\amp}{&amp;}
@@ -244,12 +247,16 @@ eBookConfig.enable_chatcodes =  false;
 <div class="toc-title-box"><a href="ch-Confidence-Intervals.html" class="internal"><span class="codenumber">4</span> <span class="title">Confidence Intervals</span></a></div>
 <ul class="structural toc-item-list">
 <li class="toc-item toc-section">
-<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Central Limit Theorem</span></a></div>
-<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
+<div class="toc-title-box"><a href="sec-Likelihood.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Likelihood</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Likelihood.html#sec-Likelihood-20" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
 </li>
 <li class="toc-item toc-section">
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+<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Central Limit Theorem</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.3</span> <span class="title">Confidence Intervals</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.3</span> <span class="title">Exercises</span></a></div></li></ul>
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sec-Independent-Events.html

@@ -62,7 +62,7 @@ window.MathJax = {
       "[pretext]/mathjaxknowl3.js"
     ],
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-      "pretext": "_static/pretext/js/lib"
+      "pretext": "_static/pretext/js"
     }
   },
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@@ -79,7 +79,7 @@ window.MathJax = {
 <meta property="og:type" content="book">
 <meta property="book:title" content="Math 1044 Notes">
 <meta property="book:author" content="Andy Eisenberg">
-<script src="_static/pretext/js/lib/jquery.min.js"></script><script src="_static/pretext/js/lib/jquery.sticky.js"></script><script src="_static/pretext/js/lib/jquery.espy.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><script src="_static/pretext/js/user_preferences.js"></script><!--** eBookCongig is necessary to configure interactive       **-->
+<script src="_static/pretext/js/jquery.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><!--** eBookCongig is necessary to configure interactive       **-->
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 eBookConfig.enableScratchAC = false;
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+<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
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 <body class="pretext book ignore-math">
@@ -151,6 +151,9 @@ eBookConfig.enable_chatcodes =  false;
 \DeclareMathOperator{\E}{E}
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 \DeclareMathOperator{\Cov}{Cov}
+\newcommand{\L}{\mathcal{L}}
+
+\newcommand{\est}{\widehat}
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 <ul class="structural toc-item-list">
 <li class="toc-item toc-section">
-<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Central Limit Theorem</span></a></div>
-<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
+<div class="toc-title-box"><a href="sec-Likelihood.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Likelihood</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Likelihood.html#sec-Likelihood-20" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
 </li>
 <li class="toc-item toc-section">
-<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Confidence Intervals</span></a></div>
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+<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Central Limit Theorem</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.3</span> <span class="title">Confidence Intervals</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.3</span> <span class="title">Exercises</span></a></div></li></ul>
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@@ -62,7 +62,7 @@ window.MathJax = {
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+\newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle     \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle        \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle      \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}}
+\)</span></div>
+<div class="ptx-page">
+<div id="ptx-sidebar" class="ptx-sidebar"><nav id="ptx-toc" class="ptx-toc depth2"><ul class="structural toc-item-list contains-active">
+<li class="toc-item toc-frontmatter"><div class="toc-title-box"><a href="frontmatter.html" class="internal"><span class="title">Front Matter</span></a></div></li>
+<li class="toc-item toc-chapter">
+<div class="toc-title-box"><a href="ch-Introduction.html" class="internal"><span class="codenumber">0</span> <span class="title">Introduction</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-section"><div class="toc-title-box"><a href="sec-Introduction.html" class="internal"><span class="codenumber">0.1</span> <span class="title">Introduction</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-chapter">
+<div class="toc-title-box"><a href="ch-Probability.html" class="internal"><span class="codenumber">1</span> <span class="title">Probability Theory</span></a></div>
+<ul class="structural toc-item-list">
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Set-Theory.html" class="internal"><span class="codenumber">1.1</span> <span class="title">Set Theory</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Set-Theory.html#exercises-Set-Theory" class="internal"><span class="codenumber">1.1</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Probability.html" class="internal"><span class="codenumber">1.2</span> <span class="title">Definition of Probability</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Probability.html#exercises-Probability" class="internal"><span class="codenumber">1.2</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Conditional-Probability.html" class="internal"><span class="codenumber">1.3</span> <span class="title">Conditional Probability</span></a></div>
+<ul class="structural toc-item-list">
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Conditional-Probability.html#subsec-conditional-probability" class="internal"><span class="codenumber">1.3.1</span> <span class="title">Conditional Probability</span></a></div></li>
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Conditional-Probability.html#subsec-diagnostic-testing" class="internal"><span class="codenumber">1.3.2</span> <span class="title">Diagnostic Testing</span></a></div></li>
+<li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Conditional-Probability.html#exercises-Conditional-Probability" class="internal"><span class="codenumber">1.3.3</span> <span class="title">Exercises</span></a></div></li>
+</ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Independent-Events.html" class="internal"><span class="codenumber">1.4</span> <span class="title">Independent Events</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Independent-Events.html#exercises-Independent-Events" class="internal"><span class="codenumber">1.4</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+</ul>
+</li>
+<li class="toc-item toc-chapter">
+<div class="toc-title-box"><a href="ch-Random-Variables.html" class="internal"><span class="codenumber">2</span> <span class="title">Random Variables</span></a></div>
+<ul class="structural toc-item-list">
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Discrete-RVs.html" class="internal"><span class="codenumber">2.1</span> <span class="title">Discrete Random Variables</span></a></div>
+<ul class="structural toc-item-list">
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Discrete-RVs.html#subsec-Discrete-RVs" class="internal"><span class="codenumber">2.1.1</span> <span class="title">Discrete Random Variables</span></a></div></li>
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Discrete-RVs.html#subsec-binomial-distribution" class="internal"><span class="codenumber">2.1.2</span> <span class="title">The Binomial Distribution</span></a></div></li>
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Discrete-RVs.html#subsec-geometric-distribution" class="internal"><span class="codenumber">2.1.3</span> <span class="title">Geometric Distribution</span></a></div></li>
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Discrete-RVs.html#subsec-poisson-distribution" class="internal"><span class="codenumber">2.1.4</span> <span class="title">Poisson Distribution</span></a></div></li>
+<li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Discrete-RVs.html#exercises-Discrete-RVs" class="internal"><span class="codenumber">2.1.5</span> <span class="title">Exercises</span></a></div></li>
+</ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Continuous-RVs.html" class="internal"><span class="codenumber">2.2</span> <span class="title">Continuous Random Variables</span></a></div>
+<ul class="structural toc-item-list">
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Continuous-RVs.html#subsec-pdfs" class="internal"><span class="codenumber">2.2.1</span> <span class="title">Probability Density Functions</span></a></div></li>
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Continuous-RVs.html#subsec-cdf" class="internal"><span class="codenumber">2.2.2</span> <span class="title">Cumulative Distribution Functions</span></a></div></li>
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Continuous-RVs.html#subsec-exponential-distribution" class="internal"><span class="codenumber">2.2.3</span> <span class="title">The Exponential Distribution</span></a></div></li>
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Continuous-RVs.html#subsec-normal-distribution" class="internal"><span class="codenumber">2.2.4</span> <span class="title">Normal Distribution</span></a></div></li>
+<li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Continuous-RVs.html#exercises-Continuous-RVs" class="internal"><span class="codenumber">2.2.5</span> <span class="title">Exercises</span></a></div></li>
+</ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Joint-Distributions.html" class="internal"><span class="codenumber">2.3</span> <span class="title">Joint Distributions</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Joint-Distributions.html#exercises-Joint-Distributions" class="internal"><span class="codenumber">2.3</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+</ul>
+</li>
+<li class="toc-item toc-chapter">
+<div class="toc-title-box"><a href="ch-Expected-Value.html" class="internal"><span class="codenumber">3</span> <span class="title">Expected Value and Variance</span></a></div>
+<ul class="structural toc-item-list">
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Expected-Value.html" class="internal"><span class="codenumber">3.1</span> <span class="title">Expected Value</span></a></div>
+<ul class="structural toc-item-list">
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Expected-Value.html#subsec-discrete-EV" class="internal"><span class="codenumber">3.1.1</span> <span class="title">Discrete Expected Value</span></a></div></li>
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Expected-Value.html#subsec-continuous-EV" class="internal"><span class="codenumber">3.1.2</span> <span class="title">Continuous Expected Value</span></a></div></li>
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Expected-Value.html#subsec-linearity-EV" class="internal"><span class="codenumber">3.1.3</span> <span class="title">Linearity of Expected Value</span></a></div></li>
+<li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Expected-Value.html#exercises-Expected-Value" class="internal"><span class="codenumber">3.1.4</span> <span class="title">Exercises</span></a></div></li>
+</ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Variance.html" class="internal"><span class="codenumber">3.2</span> <span class="title">Variance</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Variance.html#exercises-Variance" class="internal"><span class="codenumber">3.2</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Covariance.html" class="internal"><span class="codenumber">3.3</span> <span class="title">Covariance</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Covariance.html#exercises-Covariance" class="internal"><span class="codenumber">3.3</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+</ul>
+</li>
+<li class="toc-item toc-chapter contains-active">
+<div class="toc-title-box"><a href="ch-Confidence-Intervals.html" class="internal"><span class="codenumber">4</span> <span class="title">Confidence Intervals</span></a></div>
+<ul class="structural toc-item-list contains-active">
+<li class="toc-item toc-section contains-active">
+<div class="toc-title-box"><a href="sec-Likelihood.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Likelihood</span></a></div>
+<ul class="structural toc-item-list active"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Likelihood.html#sec-Likelihood-20" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Central Limit Theorem</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.3</span> <span class="title">Confidence Intervals</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.3</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+</ul>
+</li>
+<li class="toc-item toc-chapter">
+<div class="toc-title-box"><a href="ch-Hypothesis-Testing.html" class="internal"><span class="codenumber">5</span> <span class="title">Hypothesis Testing</span></a></div>
+<ul class="structural toc-item-list">
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-One-Sample-Tests.html" class="internal"><span class="codenumber">5.1</span> <span class="title">One Sample Tests</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-One-Sample-Tests.html#exercises-One-Sample-Tests" class="internal"><span class="codenumber">5.1</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Two-Sample-Tests.html" class="internal"><span class="codenumber">5.2</span> <span class="title">Two Sample Tests</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Two-Sample-Tests.html#exercises-Two-Sample-Tests" class="internal"><span class="codenumber">5.2</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Power.html" class="internal"><span class="codenumber">5.3</span> <span class="title">Power of a Test</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Power.html#exercises-Power" class="internal"><span class="codenumber">5.3</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Chi-Squared.html" class="internal"><span class="codenumber">5.4</span> <span class="title"><span class="process-math">\(\chi^2\)</span> Test</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Chi-Squared.html#exercises-Chi-Squared" class="internal"><span class="codenumber">5.4</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+</ul>
+</li>
+<li class="toc-item toc-chapter">
+<div class="toc-title-box"><a href="ch-Linear-Regression.html" class="internal"><span class="codenumber">6</span> <span class="title">Linear Regression</span></a></div>
+<ul class="structural toc-item-list">
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Correlation.html" class="internal"><span class="codenumber">6.1</span> <span class="title">Correlation</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Correlation.html#exercises-Correlation" class="internal"><span class="codenumber">6.1</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Linear-Regression.html" class="internal"><span class="codenumber">6.2</span> <span class="title">Linear Regression</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Linear-Regression.html#exercises-Linear-Regression" class="internal"><span class="codenumber">6.2</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+</ul>
+</li>
+<li class="toc-item toc-backmatter"><div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div></li>
+</ul></nav></div>
+<main class="ptx-main"><div id="ptx-content" class="ptx-content"><section class="section" id="sec-Likelihood"><h2 class="heading hide-type">
+<span class="type">Section</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.1</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Likelihood</span>
+</h2>
+<div class="para" id="sec-Likelihood-2">So far, we’ve been concerned with probability theory. Starting with a probability distribution and some parameter values, we’ve tried to answer questions like: What’s the probability of seeing certain experimental results? Statistics is concerned with going in the other direction: Upon seeing the experimental results, can we determine the type of underlying probability distribution? Can we determine its parameters?<div class="autopermalink" data-description="Paragraph"><a href="#sec-Likelihood-2" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<article class="definition definition-like" id="def-estimator"><h3 class="heading">
+<span class="type">Definition</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.1.1</span><span class="period heading-divison-mark heading-divison-mark__period">.</span>
+</h3>
+<div class="para" id="def-estimator-1-1">An <dfn class="terminology">estimator</dfn> is a value of a parameter computed from a sample of data.<div class="autopermalink" data-description="Paragraph"><a href="#def-estimator-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Definition 4.1.1"><a href="#def-estimator" title="Copy heading and permalink for Definition 4.1.1" aria-label="Copy heading and permalink for Definition 4.1.1">🔗</a></div></article><article class="example example-like" id="sec-Likelihood-4"><h3 class="heading">
+<span class="type">Example</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.1.2</span><span class="period heading-divison-mark heading-divison-mark__period">.</span>
+</h3>
+<div class="para" id="sec-Likelihood-4-1">Suppose we find a coin on the street and don’t know whether or not it’s fair. We want to know the probability <span class="process-math">\(p\)</span> of the coin coming up heads. We might, for example, flip the coin <span class="process-math">\(n\)</span> times and count the number <span class="process-math">\(k\)</span> of heads. Then, we’ll estimate <span class="process-math">\(p = \frac{k}{n}\text{.}\)</span> We’ll refer to this as a <dfn class="terminology">common sense</dfn> estimator. (Other distributions and parameter types will have different notions of "common sense".)<div class="autopermalink" data-description="Paragraph"><a href="#sec-Likelihood-4-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Example 4.1.2"><a href="#sec-Likelihood-4" title="Copy heading and permalink for Example 4.1.2" aria-label="Copy heading and permalink for Example 4.1.2">🔗</a></div></article><div class="para" id="sec-Likelihood-5">An estimator is, itself, a random variable: it produces a numerical value based on the results of an experiment. We’ll use notation like <span class="process-math">\(\est{p}\)</span> for a random variable which is an estimator for a parameter <span class="process-math">\(p\text{.}\)</span> (Similarly, <span class="process-math">\(\est{\lambda}\)</span> would denote an estimator for a parameter called <span class="process-math">\(\lambda\text{.}\)</span>)<div class="autopermalink" data-description="Paragraph"><a href="#sec-Likelihood-5" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<article class="definition definition-like" id="def-unbiased"><h3 class="heading">
+<span class="type">Definition</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.1.3</span><span class="period heading-divison-mark heading-divison-mark__period">.</span>
+</h3>
+<div class="para" id="def-unbiased-1-1">An estimator <span class="process-math">\(\est{p}\)</span> is called <dfn class="terminology">unbiased</dfn> if <span class="process-math">\(\E(\est{p}) = p\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#def-unbiased-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Definition 4.1.3"><a href="#def-unbiased" title="Copy heading and permalink for Definition 4.1.3" aria-label="Copy heading and permalink for Definition 4.1.3">🔗</a></div></article><article class="example example-like" id="sec-Likelihood-7"><h3 class="heading">
+<span class="type">Example</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.1.4</span><span class="period heading-divison-mark heading-divison-mark__period">.</span>
+</h3>
+<div class="para logical" id="sec-Likelihood-7-1-1">
+<div class="para">Suppose we have a coin with parameter <span class="process-math">\(p\text{,}\)</span> which we’ll flip <span class="process-math">\(n\)</span> times and count the number <span class="process-math">\(k\)</span> of heads. We use the unbiased estimator <span class="process-math">\(\est{p} = \frac{k}{n}\text{.}\)</span> In this case, notice that <span class="process-math">\(k \sim \Bin(n, p)\text{,}\)</span> so we know <span class="process-math">\(\E(k) = np\text{,}\)</span> although we don’t know the value of <span class="process-math">\(p\text{.}\)</span> (We probably do know the value of <span class="process-math">\(n\text{;}\)</span> after all, we’re flipping the coin!) Now:</div>
+<div class="displaymath process-math" id="sec-Likelihood-7-1-1-9">
+\begin{gather*}
+\E(\est{p}) = \E\left(\frac{k}{n}\right) = \frac{1}{n} \cdot \E(k) = \frac{1}{n} \cdot np = p. 
+\end{gather*}
+</div>
+<div class="para">It’s worth pausing for a moment to be appropriately impressed with ourselves. We still don’t know the true value of <span class="process-math">\(p\text{.}\)</span> But we managed to show that our common sense method of estimating <span class="process-math">\(p\)</span> gives, on average, the correct value.</div>
+<div class="autopermalink" data-description="Paragraph"><a href="#sec-Likelihood-7-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Example 4.1.4"><a href="#sec-Likelihood-7" title="Copy heading and permalink for Example 4.1.4" aria-label="Copy heading and permalink for Example 4.1.4">🔗</a></div></article><div class="para" id="sec-Likelihood-8">We’d like to be able to collect some data and use that data to estimate the values of whatever parameters our distribution has. Perhaps as a starting point, it would be good to identify the single most likely value of a parameter:<div class="autopermalink" data-description="Paragraph"><a href="#sec-Likelihood-8" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<article class="definition definition-like" id="def-likelihood"><h3 class="heading">
+<span class="type">Definition</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.1.5</span><span class="period heading-divison-mark heading-divison-mark__period">.</span>
+</h3>
+<div class="para logical" id="def-likelihood-1-1">
+<div class="para">Suppose we collect some data to estimate a parameter <span class="process-math">\(p\text{.}\)</span> The <dfn class="terminology">likelihood function</dfn> is:</div>
+<div class="displaymath process-math" id="def-likelihood-1-1-3">
+\begin{gather*}
+\L(p) = \Pr(\text{data} \mid \text{parameter value is } p). 
+\end{gather*}
+</div>
+<div class="para">The value of <span class="process-math">\(p\)</span> which maximizes the function <span class="process-math">\(\L(p)\)</span> is called the <dfn class="terminology">maximum likelihood estimation</dfn>, or <dfn class="terminology">MLE</dfn>, of <span class="process-math">\(p\text{.}\)</span>
+</div>
+<div class="autopermalink" data-description="Paragraph"><a href="#def-likelihood-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Definition 4.1.5"><a href="#def-likelihood" title="Copy heading and permalink for Definition 4.1.5" aria-label="Copy heading and permalink for Definition 4.1.5">🔗</a></div></article><article class="example example-like" id="sec-Likelihood-10"><h3 class="heading">
+<span class="type">Example</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.1.6</span><span class="period heading-divison-mark heading-divison-mark__period">.</span>
+</h3>
+<div class="para logical" id="sec-Likelihood-10-1-1">
+<div class="para">Suppose we flip a coin 100 times. Let <span class="process-math">\(N\)</span> be the number of heads. Then <span class="process-math">\(N\sim \Bin(100, p)\)</span> for some unknown value of <span class="process-math">\(p\text{:}\)</span>
+</div>
+<div class="displaymath process-math" id="sec-Likelihood-10-1-1-4">
+\begin{align*}
+\Pr(N = k) \amp = b(k; 100, p) = {100 \choose k} p^k (1 - p)^{100 - k} 
+\end{align*}
+</div>
+<div class="para">In this case, <span class="process-math">\(k\)</span> is the data that we collect, and <span class="process-math">\(p\)</span> is the value of the parameter. Suppose we see <span class="process-math">\(52\)</span> heads. Then:</div>
+<div class="displaymath process-math" id="sec-Likelihood-10-1-1-8">
+\begin{gather*}
+\L(p) = {100 \choose 52} p^{52} (1 - p)^{48}. 
+\end{gather*}
+</div>
+<div class="para">If we want to know the most likely value of the parameter <span class="process-math">\(p\text{,}\)</span> then we should maximize <span class="process-math">\(\L(p)\)</span> over the interval <span class="process-math">\(0 \leq p \leq 1\text{.}\)</span>
+</div>
+<div class="displaymath process-math" id="sec-Likelihood-10-1-1-12">
+\begin{align*}
+\L'(p) \amp = {100 \choose 52} \left[ 52 p^{51}(1 - p)^{48} + p^{52} 48 (1 - p)^{47}(-1)\right] \\
+\amp = {100 \choose 52} p^{51} (1 - p)^{47} \left[ 52 (1 - p) -  48p \right] \\
+\amp = {100 \choose 52} p^{51} (1 - p)^{47} \left[ 52 - 100 p \right]. 
+\end{align*}
+</div>
+<div class="para">We can see that <span class="process-math">\(\L'(p) = 0\)</span> when <span class="process-math">\(p = 0, 1, \frac{52}{100}\text{,}\)</span> and the endpoints of the interval we’re maximizing over are <span class="process-math">\(p = 0, 1\text{,}\)</span> so we can build a table:</div>
+<div class="autopermalink" data-description="Paragraph"><a href="#sec-Likelihood-10-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div> <figure class="table table-like" id="sec-Likelihood-10-1-2"><figcaption><span class="type">Table</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.1.7<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span>Looking for the Maximum<div class="autopermalink" data-description="Table 4.1.7: Looking for the Maximum"><a href="#sec-Likelihood-10-1-2" title="Copy heading and permalink for Table 4.1.7: Looking for the Maximum" aria-label="Copy heading and permalink for Table 4.1.7: Looking for the Maximum">🔗</a></div></figcaption><div class="tabular-box natural-width"><table class="tabular">
+<tr>
+<td class="c m b1 r0 l0 t0 lines"><span class="process-math">\(p\)</span></td>
+<td class="c m b1 r0 l0 t0 lines"><span class="process-math">\(\L(p)\)</span></td>
+</tr>
+<tr>
+<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(0\)</span></td>
+<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(0\)</span></td>
+</tr>
+<tr>
+<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(52/100\)</span></td>
+<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(\gt 0\)</span></td>
+</tr>
+<tr>
+<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(1\)</span></td>
+<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(0\)</span></td>
+</tr>
+</table></div></figure> <div class="para" id="sec-Likelihood-10-1-3">Note that we don’t need to know the exact value of <span class="process-math">\(\L(52/100)\)</span> in order to see that it’s strictly positive, and therefore the maximum value of <span class="process-math">\(\L(p)\text{.}\)</span> So, the MLE of <span class="process-math">\(p\)</span> is <span class="process-math">\(52/100\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#sec-Likelihood-10-1-3" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Example 4.1.6"><a href="#sec-Likelihood-10" title="Copy heading and permalink for Example 4.1.6" aria-label="Copy heading and permalink for Example 4.1.6">🔗</a></div></article><div class="para" id="sec-Likelihood-11">We can see in the previous example that the MLE of <span class="process-math">\(p\)</span> is also the common sense estimation of <span class="process-math">\(p\text{.}\)</span> This will be the case in general for the binomial distribution, so we won’t need to redo this work over and over:<div class="autopermalink" data-description="Paragraph"><a href="#sec-Likelihood-11" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<article class="fact theorem-like" id="fact-MLE-binomial"><h3 class="heading">
+<span class="type">Fact</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.1.8</span><span class="period heading-divison-mark heading-divison-mark__period">.</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Binomial MLE.</span>
+</h3>
+<div class="para" id="fact-MLE-binomial-2-1">If we see <span class="process-math">\(k\)</span> heads in <span class="process-math">\(n\)</span> coin flips, then the MLE of the bias <span class="process-math">\(p\)</span> is <span class="process-math">\(\frac{k}{n}\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#fact-MLE-binomial-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Fact 4.1.8: Binomial MLE"><a href="#fact-MLE-binomial" title="Copy heading and permalink for Fact 4.1.8: Binomial MLE" aria-label="Copy heading and permalink for Fact 4.1.8: Binomial MLE">🔗</a></div></article><div class="para" id="sec-Likelihood-13">As we remember from Calculus 1, maximizing a continuous function works slightly differently over a closed interval (like the previous example) or an open interval (like the next example).<div class="autopermalink" data-description="Paragraph"><a href="#sec-Likelihood-13" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<article class="example example-like" id="sec-Likelihood-14"><h3 class="heading">
+<span class="type">Example</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.1.9</span><span class="period heading-divison-mark heading-divison-mark__period">.</span>
+</h3>
+<div class="para logical" id="sec-Likelihood-14-1-1">
+<div class="para">Suppose a radioactive material emits particles as it decays. Let <span class="process-math">\(N\)</span> count the particles emitted. Then <span class="process-math">\(N \sim \Poiss(\lambda)\)</span> for some unknown rate parameter <span class="process-math">\(\lambda\text{:}\)</span>
+</div>
+<div class="displaymath process-math" id="sec-Likelihood-14-1-1-4">
+\begin{gather*}
+\Pr(N = k) = p(k; \lambda) = \frac{\lambda^k}{k!} e^{-\lambda} 
+\end{gather*}
+</div>
+<div class="para">Suppose we observe a sample of material for 1 hour and count 8 particles emitted. Then:</div>
+<div class="displaymath process-math" id="sec-Likelihood-14-1-1-5">
+\begin{gather*}
+\L(\lambda) = \frac{\lambda^8}{8!} e^{-\lambda} 
+\end{gather*}
+</div>
+<div class="para">To maximize <span class="process-math">\(\L(\lambda)\)</span> over the interval <span class="process-math">\(0 \lt \lambda \lt \infty\text{,}\)</span> we start by finding critical points.</div>
+<div class="displaymath process-math" id="sec-Likelihood-14-1-1-8">
+\begin{align*}
+\L'(\lambda) \amp = \frac{1}{8!} \left[ 8 \lambda^7 e^{-\lambda} + \lambda^8 e^{-\lambda} (-1)\right] \\
+\amp = \frac{1}{8!} \lambda^7 e^{-\lambda} \left[ 8 - e^{-\lambda} \right] 
+\end{align*}
+</div>
+<div class="para">The only critical point is <span class="process-math">\(\lambda = 8\text{,}\)</span> but we have not justified that this is the location of a global maximum. A critical point is only a potential location of a local minimum or maximum. But with a bit more justification: observe that <span class="process-math">\(\L'\)</span> is positive on the interval <span class="process-math">\((0, 8)\)</span> and negative on the interval <span class="process-math">\((8, \infty)\text{.}\)</span> Therefore the function <span class="process-math">\(\L\)</span> increases on <span class="process-math">\((0, 8)\)</span> and decreases on <span class="process-math">\((8, \infty)\text{.}\)</span> So it must reach its maximum at <span class="process-math">\(\lambda = 8\text{,}\)</span> which is therefore the MLE.</div>
+<div class="autopermalink" data-description="Paragraph"><a href="#sec-Likelihood-14-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Example 4.1.9"><a href="#sec-Likelihood-14" title="Copy heading and permalink for Example 4.1.9" aria-label="Copy heading and permalink for Example 4.1.9">🔗</a></div></article><div class="para" id="sec-Likelihood-15">As with the binomial distribution, the calculation will be essentially the same regardless of the specific number of particles observed, so:<div class="autopermalink" data-description="Paragraph"><a href="#sec-Likelihood-15" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<article class="fact theorem-like" id="fact-MLE-Poisson"><h3 class="heading">
+<span class="type">Fact</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.1.10</span><span class="period heading-divison-mark heading-divison-mark__period">.</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Poisson MLE.</span>
+</h3>
+<div class="para" id="fact-MLE-Poisson-2-1">If we observe a Poisson process and see <span class="process-math">\(k\)</span> events occur, then the MLE of the rate parameter <span class="process-math">\(\lambda\)</span> is <span class="process-math">\(k\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#fact-MLE-Poisson-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Fact 4.1.10: Poisson MLE"><a href="#fact-MLE-Poisson" title="Copy heading and permalink for Fact 4.1.10: Poisson MLE" aria-label="Copy heading and permalink for Fact 4.1.10: Poisson MLE">🔗</a></div></article><div class="para" id="sec-Likelihood-17">The situation for continuous random variables is similar, but slightly different. To build the likelihood function, we should use the pdf of the continuous random variable. So the likelihood function will give the probabiliy density given the data collected, rather than the probability itself.<div class="autopermalink" data-description="Paragraph"><a href="#sec-Likelihood-17" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<article class="example example-like" id="example-exponential-MLE"><h3 class="heading">
+<span class="type">Example</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.1.11</span><span class="period heading-divison-mark heading-divison-mark__period">.</span>
+</h3>
+<div class="para logical" id="example-exponential-MLE-1-1">
+<div class="para">Suppose we observe a cell and measure the time <span class="process-math">\(T\)</span> until a toxin molecule leaves the cell. Then <span class="process-math">\(T \sim \Exp(\lambda)\)</span> for some unknown rate parameter <span class="process-math">\(\lambda\text{:}\)</span>
+</div>
+<div class="displaymath process-math" id="example-exponential-MLE-1-1-4">
+\begin{gather*}
+f(t) = \lambda e^{-\lambda t}. 
+\end{gather*}
+</div>
+<div class="para">Suppose we observe a molecule leave the cell at <span class="process-math">\(t = 0.3\)</span> minutes. Then:</div>
+<div class="displaymath process-math" id="example-exponential-MLE-1-1-6">
+\begin{align*}
+L(\lambda) \amp = \lambda e^{-0.3\lambda} \\
+L'(\lambda) \amp = e^{-0.3\lambda} + \lambda e^{-0.3t} (-0.3) \\
+\amp = e^{-0.3\lambda}\left[ 1 - 0.3\lambda\right] 
+\end{align*}
+</div>
+<div class="para">The critical point is <span class="process-math">\(\lambda = \frac{1}{0.3} \approx 3.33\text{.}\)</span> Since <span class="process-math">\(\L' \gt 0\)</span> on <span class="process-math">\((0, 3.33)\)</span> and <span class="process-math">\(\L' \lt 0\)</span> on <span class="process-math">\((3.33, \infty)\text{,}\)</span> there is a global maximum at <span class="process-math">\(\lambda \approx 3.33\text{,}\)</span> which is therefore the MLE.</div>
+<div class="autopermalink" data-description="Paragraph"><a href="#example-exponential-MLE-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div> <div class="para" id="example-exponential-MLE-1-2">The specific time <span class="process-math">\(0.3\)</span> minutes doesn’t particularly matter in this calculation. Whatever the time <span class="process-math">\(t\text{,}\)</span> essentially the same calculation will result in a MLE of <span class="process-math">\(\lambda = 1/t\text{.}\)</span> But what if we collect multiple pieces of data?<div class="autopermalink" data-description="Paragraph"><a href="#example-exponential-MLE-1-2" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div> <figure class="table table-like" id="example-exponential-MLE-1-3"><figcaption><span class="type">Table</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.1.12<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span>Time Data<div class="autopermalink" data-description="Table 4.1.12: Time Data"><a href="#example-exponential-MLE-1-3" title="Copy heading and permalink for Table 4.1.12: Time Data" aria-label="Copy heading and permalink for Table 4.1.12: Time Data">🔗</a></div></figcaption><div class="tabular-box natural-width"><table class="tabular">
+<tr>
+<td class="c m b1 r0 l0 t0 lines">Molecule</td>
+<td class="c m b1 r0 l0 t0 lines">Waiting Time</td>
+<td class="c m b1 r0 l0 t0 lines">Rate Estimation</td>
+</tr>
+<tr>
+<td class="c m b0 r0 l0 t0 lines">1</td>
+<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(0.3\)</span></td>
+<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(3.33\)</span></td>
+</tr>
+<tr>
+<td class="c m b0 r0 l0 t0 lines">2</td>
+<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(0.8\)</span></td>
+<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(1.25\)</span></td>
+</tr>
+<tr>
+<td class="c m b0 r0 l0 t0 lines">3</td>
+<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(0.5\)</span></td>
+<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(2.00\)</span></td>
+</tr>
+<tr>
+<td class="c m b0 r0 l0 t0 lines">4</td>
+<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(0.6\)</span></td>
+<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(1.67\)</span></td>
+</tr>
+<tr>
+<td class="c m b0 r0 l0 t0 lines">5</td>
+<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(0.9\)</span></td>
+<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(1.11\)</span></td>
+</tr>
+</table></div></figure> <div class="para" id="example-exponential-MLE-1-4">How should take all of this data into account in our maximum likelihood estimation? We might consider taking the average of all of the separate rate estimations, which would give <span class="process-math">\(1.87\text{.}\)</span> Is this the most likely? We need some mathematical justification.<div class="autopermalink" data-description="Paragraph"><a href="#example-exponential-MLE-1-4" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div> <div class="para logical" id="example-exponential-MLE-1-5">
+<div class="para">To account for multiple, independent data points, we should multiply the probability densities for each in the creation of our likelihood function:</div>
+<div class="displaymath process-math" id="example-exponential-MLE-1-5-1">
+\begin{align*}
+\L(\lambda) \amp = \left(\lambda e^{-0.3\lambda}\right)\left(\lambda e^{-0.8\lambda}\right)\left(\lambda e^{-0.5\lambda}\right)\left(\lambda e^{-0.6\lambda}\right)\left(\lambda e^{-0.9\lambda}\right) \\
+\amp = \lambda^5 e^{-0.3\lambda - 0.8\lambda - 0.5\lambda - 0.6\lambda - 0.9\lambda } \\
+\amp = \lambda^5 e^{-3.1\lambda} 
+\end{align*}
+</div>
+<div class="para">Now we can find the maximum:</div>
+<div class="displaymath process-math" id="example-exponential-MLE-1-5-2">
+\begin{align*}
+\L'(\lambda) \amp = 5 \lambda^4 e^{-3.1\lambda} + \lambda^5 e^{-3.1\lambda} (-3.1) \\
+\amp = 5 \lambda^4 e^{-3.1\lambda} + \lambda^5 e^{-3.1\lambda} (-3.1) \\
+\amp = \lambda^4 e^{-3.1\lambda} \left[5 - 3.1\lambda \right] 
+\end{align*}
+</div>
+<div class="para">The only critical point is <span class="process-math">\(5/3.1 \approx 1.61\text{.}\)</span> Since <span class="process-math">\(\L' \gt 0\)</span> on <span class="process-math">\((0, 1.61)\)</span> and <span class="process-math">\(\L' \lt 0\)</span> on <span class="process-math">\((1.61, \infty)\text{,}\)</span> there is a global maximum at <span class="process-math">\(\lambda = 1.61\text{,}\)</span> which is therefore the MLE.</div>
+<div class="autopermalink" data-description="Paragraph"><a href="#example-exponential-MLE-1-5" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div> <div class="para" id="example-exponential-MLE-1-6">It may seem less clear how to generalize this calculation for other tables of data. Observe that the value <span class="process-math">\(3.1\)</span> is the sum of the five times in the table, so <span class="process-math">\(3.1/5\)</span> is the average time. The MLE turned out to be the reciprocal of the average time (just as the MLE with only one data point was the reciprocal of that one time). Notice that this does <em class="emphasis">not</em> match the guess we made previously of averaging the individual rate estimations for each data point.<div class="autopermalink" data-description="Paragraph"><a href="#example-exponential-MLE-1-6" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Example 4.1.11"><a href="#example-exponential-MLE" title="Copy heading and permalink for Example 4.1.11" aria-label="Copy heading and permalink for Example 4.1.11">🔗</a></div></article><article class="fact theorem-like" id="fact-MLE-exponential"><h3 class="heading">
+<span class="type">Fact</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.1.13</span><span class="period heading-divison-mark heading-divison-mark__period">.</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Exponential MLE.</span>
+</h3>
+<div class="para" id="fact-MLE-exponential-2-1">If we observe a Poisson process and see events occur after waiting times <span class="process-math">\(t_1, t_2, \dotsc, t_n\text{,}\)</span> then the MLE of the rate parameter <span class="process-math">\(\lambda\)</span> is <span class="process-math">\(\frac{n}{t_1 + t_2 + \dotsb + t_n}\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#fact-MLE-exponential-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Fact 4.1.13: Exponential MLE"><a href="#fact-MLE-exponential" title="Copy heading and permalink for Fact 4.1.13: Exponential MLE" aria-label="Copy heading and permalink for Fact 4.1.13: Exponential MLE">🔗</a></div></article><section class="exercises" id="sec-Likelihood-20"><h3 class="heading hide-type">
+<span class="type">Exercises</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber"></span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Exercises</span>
+</h3>
+<article class="exercise exercise-like" id="sec-Likelihood-20-1"><h4 class="heading"><span class="codenumber">1<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
+<div class="para" id="sec-Likelihood-20-1-1-1">Suppose a coin has an unknown probability of coming up heads. We perform the experiment in five independent trials, during which it takes 4, 5, 4, 3, and 6 flips to see our first heads in each trial. What is the maximum likelihood estimation for the probability of the coin coming up heads on a flip?<div class="autopermalink" data-description="Paragraph"><a href="#sec-Likelihood-20-1-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Exercise 4.1.1"><a href="#sec-Likelihood-20-1" title="Copy heading and permalink for Exercise 4.1.1" aria-label="Copy heading and permalink for Exercise 4.1.1">🔗</a></div></article><article class="exercise exercise-like" id="sec-Likelihood-20-2"><h4 class="heading"><span class="codenumber">2<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
+<div class="para" id="sec-Likelihood-20-2-1-1">Suppose a coin has an unknown probability of coming up heads. We perform the experiment in <span class="process-math">\(n\)</span> independent trials, during which it takes <span class="process-math">\(k_1, k_2, \dotsc, k_n\)</span> flips to see our first heads in each trial. Find a "common sense" MLE formula for the geometric distribution.<div class="autopermalink" data-description="Paragraph"><a href="#sec-Likelihood-20-2-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="solutions"><details id="sec-Likelihood-20-2-2" class="hint solution-like born-hidden-knowl"><summary class="knowl__link"><span class="type">Hint</span><span class="period heading-divison-mark heading-divison-mark__period">.</span></summary><div class="hint solution-like knowl__content">
+<div class="para" id="sec-Likelihood-20-2-2-1">You <em class="emphasis">could</em> set up a calculation analogous to <a href="sec-Likelihood.html#example-exponential-MLE" class="xref" data-knowl="./knowl/xref/example-exponential-MLE.html" data-reveal-label="Reveal" data-close-label="Close" title="Example 4.1.11">Example 4.1.11</a>. Or, you could consider <a href="sec-Likelihood.html#fact-MLE-binomial" class="xref" data-knowl="./knowl/xref/fact-MLE-binomial.html" data-reveal-label="Reveal" data-close-label="Close" title="Fact 4.1.8: Binomial MLE">Fact 4.1.8</a>.<div class="autopermalink" data-description="Paragraph"><a href="#sec-Likelihood-20-2-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Hint 4.1.2.1"><a href="#sec-Likelihood-20-2-2" title="Copy heading and permalink for Hint 4.1.2.1" aria-label="Copy heading and permalink for Hint 4.1.2.1">🔗</a></div>
+</div></details></div>
+<div class="autopermalink" data-description="Exercise 4.1.2"><a href="#sec-Likelihood-20-2" title="Copy heading and permalink for Exercise 4.1.2" aria-label="Copy heading and permalink for Exercise 4.1.2">🔗</a></div></article><article class="exercise exercise-like" id="sec-Likelihood-20-3"><h4 class="heading"><span class="codenumber">3<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
+<div class="para" id="sec-Likelihood-20-3-1-1">A particular store owner wants to approximate the average hourly rate at which customers come into the store. They observe 80 customers enter during a particular 4-hour shift. What is the maximum likelihood estimation for the hourly customer rate?<div class="autopermalink" data-description="Paragraph"><a href="#sec-Likelihood-20-3-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Exercise 4.1.3"><a href="#sec-Likelihood-20-3" title="Copy heading and permalink for Exercise 4.1.3" aria-label="Copy heading and permalink for Exercise 4.1.3">🔗</a></div></article><article class="exercise exercise-like" id="sec-Likelihood-20-4"><h4 class="heading"><span class="codenumber">4<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
+<div class="para" id="sec-Likelihood-20-4-1-1">A radioactive material emits particles at an unknown probabilistic rate <span class="process-math">\(\lambda\)</span> particles per minute. We observe particles emitted at times 1.1, 1.7, 1.3, 2.2, 1.9, and 1.8 minutes. Write the likelihood function <span class="process-math">\(\mathcal{L}(\lambda)\)</span> based on this data. What is the maximum likelihood estimation for <span class="process-math">\(\lambda\text{?}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#sec-Likelihood-20-4-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Exercise 4.1.4"><a href="#sec-Likelihood-20-4" title="Copy heading and permalink for Exercise 4.1.4" aria-label="Copy heading and permalink for Exercise 4.1.4">🔗</a></div></article><article class="exercise exercise-like" id="sec-Likelihood-20-5"><h4 class="heading"><span class="codenumber">5<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
+<div class="para" id="sec-Likelihood-20-5-1-1">Suppose a parameter <span class="process-math">\(\theta\)</span> takes values in <span class="process-math">\([0, 1]\)</span> with likelihood function <span class="process-math">\(\mathcal{L}(\theta) = \sqrt{\theta} - \theta^2\text{.}\)</span> Find the maximum likelihood estimation of <span class="process-math">\(\theta\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#sec-Likelihood-20-5-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Exercise 4.1.5"><a href="#sec-Likelihood-20-5" title="Copy heading and permalink for Exercise 4.1.5" aria-label="Copy heading and permalink for Exercise 4.1.5">🔗</a></div></article><div class="autopermalink" data-description="Exercises 4.1"><a href="#sec-Likelihood-20" title="Copy heading and permalink for Exercises 4.1" aria-label="Copy heading and permalink for Exercises 4.1">🔗</a></div></section><div class="autopermalink" data-description="Section 4.1: Likelihood"><a href="#sec-Likelihood" title="Copy heading and permalink for Section 4.1: Likelihood" aria-label="Copy heading and permalink for Section 4.1: Likelihood">🔗</a></div></section></div>
+<div id="ptx-content-footer" class="ptx-content-footer">
+<a class="previous-button button" href="ch-Confidence-Intervals.html" title="Previous"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe5cb;</span><span class="name">Prev</span></a><a class="top-button button" href="#" title="Top"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe5ce;</span><span class="name">Top</span></a><a class="next-button button" href="sec-CLT.html" title="Next"><span class="name">Next</span><span class="icon material-symbols-outlined" aria-hidden="true">&#xe5cc;</span></a>
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+<div id="ptx-page-footer" class="ptx-page-footer">
+<a class="pretext-link" href="https://pretextbook.org" title="PreTeXt"><div class="logo"><svg xmlns="http://www.w3.org/2000/svg" height="100%" viewBox="338 3000 8772 6866" role="img"><title>PreTeXt logo</title><g style="stroke-width:.025in; stroke:currentColor; fill:none"><polyline points="472,3590 472,9732 " style="stroke-width:174; stroke-linejoin:miter; stroke-linecap:round; "></polyline><path style="stroke-width:126;stroke-linecap:butt;" d="M 4724,9448 A 4660 4660  0  0  1  8598  9259"></path><path style="stroke-width:174;stroke-linecap:butt;" d="M 4488,9685 A 4228 4228  0  0  0   472  9732"></path><path style="stroke-width:126;stroke-linecap:butt;" d="M 4724,3590 A 4241 4241  0  0  1  8598  3496"></path><path style="stroke-width:126;stroke-linecap:round;" d="M 850,3496  A 4241 4241  0  0  1  4724  3590"></path><path style="stroke-width:126;stroke-linecap:round;" d="M 850,9259  A 4507 4507  0  0  1  4724  9448"></path><polyline points="5385,4299 4062,8125" style="stroke-width:300; stroke-linejoin:miter; stroke-linecap:round;"></polyline><polyline points="8598,3496 8598,9259" style="stroke-width:126; stroke-linejoin:miter; stroke-linecap:round;"></polyline><polyline points="850,3496 850,9259" style="stroke-width:126; stroke-linejoin:miter; stroke-linecap:round;"></polyline><polyline points="4960,9685 4488,9685" style="stroke-width:174; stroke-linejoin:miter; stroke-linecap:round;"></polyline><polyline points="3070,4582 1889,6141 3070,7700" style="stroke-width:300; stroke-linejoin:miter; stroke-linecap:round;"></polyline><polyline points="6418,4582 7600,6141 6418,7700" style="stroke-width:300; stroke-linejoin:miter; stroke-linecap:round;"></polyline><polyline points="8976,3590 8976,9732" style="stroke-width:174; stroke-linejoin:miter; stroke-linecap:round;"></polyline><path style="stroke-width:174;stroke-linecap:butt;" d="M 4960,9685 A 4228 4228  0  0  1  8976  9732"></path></g></svg></div></a><a class="runestone-link" href="https://runestone.academy" title="Runestone Academy"><img class="logo" src="https://runestone.academy/runestone/static/images/RAIcon_cropped.png" alt="Runstone Academy logo"></a><a class="mathjax-link" href="https://www.mathjax.org" title="MathJax"><img class="logo" src="https://www.mathjax.org/badge/badge-square-2.png" alt="MathJax logo"></a>
+</div>
+</body>
+</html>

sec-Linear-Regression.html

@@ -62,7 +62,7 @@ window.MathJax = {
       "[pretext]/mathjaxknowl3.js"
     ],
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-      "pretext": "_static/pretext/js/lib"
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+<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
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 <body class="pretext book ignore-math">
@@ -151,6 +151,9 @@ eBookConfig.enable_chatcodes =  false;
 \DeclareMathOperator{\E}{E}
 \DeclareMathOperator{\Var}{Var}
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+\newcommand{\L}{\mathcal{L}}
+
+\newcommand{\est}{\widehat}
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 \newcommand{\gt}{&gt;}
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@@ -244,12 +247,16 @@ eBookConfig.enable_chatcodes =  false;
 <div class="toc-title-box"><a href="ch-Confidence-Intervals.html" class="internal"><span class="codenumber">4</span> <span class="title">Confidence Intervals</span></a></div>
 <ul class="structural toc-item-list">
 <li class="toc-item toc-section">
-<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Central Limit Theorem</span></a></div>
-<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
+<div class="toc-title-box"><a href="sec-Likelihood.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Likelihood</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Likelihood.html#sec-Likelihood-20" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
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 <li class="toc-item toc-section">
-<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Confidence Intervals</span></a></div>
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+<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Central Limit Theorem</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.3</span> <span class="title">Confidence Intervals</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.3</span> <span class="title">Exercises</span></a></div></li></ul>
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sec-One-Sample-Tests.html

@@ -62,7 +62,7 @@ window.MathJax = {
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     ],
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-      "pretext": "_static/pretext/js/lib"
+      "pretext": "_static/pretext/js"
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+<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
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 <body class="pretext book ignore-math">
@@ -151,6 +151,9 @@ eBookConfig.enable_chatcodes =  false;
 \DeclareMathOperator{\E}{E}
 \DeclareMathOperator{\Var}{Var}
 \DeclareMathOperator{\Cov}{Cov}
+\newcommand{\L}{\mathcal{L}}
+
+\newcommand{\est}{\widehat}
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@@ -244,12 +247,16 @@ eBookConfig.enable_chatcodes =  false;
 <div class="toc-title-box"><a href="ch-Confidence-Intervals.html" class="internal"><span class="codenumber">4</span> <span class="title">Confidence Intervals</span></a></div>
 <ul class="structural toc-item-list">
 <li class="toc-item toc-section">
-<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Central Limit Theorem</span></a></div>
-<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
+<div class="toc-title-box"><a href="sec-Likelihood.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Likelihood</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Likelihood.html#sec-Likelihood-20" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
 </li>
 <li class="toc-item toc-section">
-<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Confidence Intervals</span></a></div>
-<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
+<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Central Limit Theorem</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.3</span> <span class="title">Confidence Intervals</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.3</span> <span class="title">Exercises</span></a></div></li></ul>
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sec-Power.html

@@ -62,7 +62,7 @@ window.MathJax = {
       "[pretext]/mathjaxknowl3.js"
     ],
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-      "pretext": "_static/pretext/js/lib"
+      "pretext": "_static/pretext/js"
     }
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@@ -79,7 +79,7 @@ window.MathJax = {
 <meta property="og:type" content="book">
 <meta property="book:title" content="Math 1044 Notes">
 <meta property="book:author" content="Andy Eisenberg">
-<script src="_static/pretext/js/lib/jquery.min.js"></script><script src="_static/pretext/js/lib/jquery.sticky.js"></script><script src="_static/pretext/js/lib/jquery.espy.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><script src="_static/pretext/js/user_preferences.js"></script><!--** eBookCongig is necessary to configure interactive       **-->
+<script src="_static/pretext/js/jquery.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><!--** eBookCongig is necessary to configure interactive       **-->
 <!--** Runestone components to run locally in reader's browser **-->
 <!--** No external communication:                              **-->
 <!--**     log level is 0, Runestone Services are disabled     **-->
@@ -101,16 +101,16 @@ eBookConfig.allow_pairs = false;
 eBookConfig.enableScratchAC = false;
 eBookConfig.build_info = "";
 eBookConfig.python3 = null;
-eBookConfig.runestone_version = '7.11.11';
+eBookConfig.runestone_version = '7.11.13';
 eBookConfig.jobehost = '';
 eBookConfig.proxyuri_runs = '';
 eBookConfig.proxyuri_files = '';
 eBookConfig.enable_chatcodes =  false;
 </script>
 <!--*** Runestone Services ***-->
-<script src="_static/prefix-runtime.fc0e080e84d54281.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
+<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
 <link rel="stylesheet" type="text/css" href="_static/prefix-runestone.6ec5960970d8b364.css">
-<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/lib/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
+<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
 </script>
 </head>
 <body class="pretext book ignore-math">
@@ -151,6 +151,9 @@ eBookConfig.enable_chatcodes =  false;
 \DeclareMathOperator{\E}{E}
 \DeclareMathOperator{\Var}{Var}
 \DeclareMathOperator{\Cov}{Cov}
+\newcommand{\L}{\mathcal{L}}
+
+\newcommand{\est}{\widehat}
 \newcommand{\lt}{&lt;}
 \newcommand{\gt}{&gt;}
 \newcommand{\amp}{&amp;}
@@ -244,12 +247,16 @@ eBookConfig.enable_chatcodes =  false;
 <div class="toc-title-box"><a href="ch-Confidence-Intervals.html" class="internal"><span class="codenumber">4</span> <span class="title">Confidence Intervals</span></a></div>
 <ul class="structural toc-item-list">
 <li class="toc-item toc-section">
-<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Central Limit Theorem</span></a></div>
-<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
+<div class="toc-title-box"><a href="sec-Likelihood.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Likelihood</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Likelihood.html#sec-Likelihood-20" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
 </li>
 <li class="toc-item toc-section">
-<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Confidence Intervals</span></a></div>
-<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
+<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Central Limit Theorem</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.3</span> <span class="title">Confidence Intervals</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.3</span> <span class="title">Exercises</span></a></div></li></ul>
 </li>
 </ul>
 </li>

sec-Probability.html

@@ -62,7 +62,7 @@ window.MathJax = {
       "[pretext]/mathjaxknowl3.js"
     ],
     "paths": {
-      "pretext": "_static/pretext/js/lib"
+      "pretext": "_static/pretext/js"
     }
   },
   "startup": {
@@ -79,7 +79,7 @@ window.MathJax = {
 <meta property="og:type" content="book">
 <meta property="book:title" content="Math 1044 Notes">
 <meta property="book:author" content="Andy Eisenberg">
-<script src="_static/pretext/js/lib/jquery.min.js"></script><script src="_static/pretext/js/lib/jquery.sticky.js"></script><script src="_static/pretext/js/lib/jquery.espy.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><script src="_static/pretext/js/user_preferences.js"></script><!--** eBookCongig is necessary to configure interactive       **-->
+<script src="_static/pretext/js/jquery.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><!--** eBookCongig is necessary to configure interactive       **-->
 <!--** Runestone components to run locally in reader's browser **-->
 <!--** No external communication:                              **-->
 <!--**     log level is 0, Runestone Services are disabled     **-->
@@ -101,16 +101,16 @@ eBookConfig.allow_pairs = false;
 eBookConfig.enableScratchAC = false;
 eBookConfig.build_info = "";
 eBookConfig.python3 = null;
-eBookConfig.runestone_version = '7.11.11';
+eBookConfig.runestone_version = '7.11.13';
 eBookConfig.jobehost = '';
 eBookConfig.proxyuri_runs = '';
 eBookConfig.proxyuri_files = '';
 eBookConfig.enable_chatcodes =  false;
 </script>
 <!--*** Runestone Services ***-->
-<script src="_static/prefix-runtime.fc0e080e84d54281.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
+<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
 <link rel="stylesheet" type="text/css" href="_static/prefix-runestone.6ec5960970d8b364.css">
-<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/lib/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
+<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
 </script>
 </head>
 <body class="pretext book ignore-math">
@@ -151,6 +151,9 @@ eBookConfig.enable_chatcodes =  false;
 \DeclareMathOperator{\E}{E}
 \DeclareMathOperator{\Var}{Var}
 \DeclareMathOperator{\Cov}{Cov}
+\newcommand{\L}{\mathcal{L}}
+
+\newcommand{\est}{\widehat}
 \newcommand{\lt}{&lt;}
 \newcommand{\gt}{&gt;}
 \newcommand{\amp}{&amp;}
@@ -244,12 +247,16 @@ eBookConfig.enable_chatcodes =  false;
 <div class="toc-title-box"><a href="ch-Confidence-Intervals.html" class="internal"><span class="codenumber">4</span> <span class="title">Confidence Intervals</span></a></div>
 <ul class="structural toc-item-list">
 <li class="toc-item toc-section">
-<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Central Limit Theorem</span></a></div>
-<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
+<div class="toc-title-box"><a href="sec-Likelihood.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Likelihood</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Likelihood.html#sec-Likelihood-20" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
 </li>
 <li class="toc-item toc-section">
-<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Confidence Intervals</span></a></div>
-<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
+<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Central Limit Theorem</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.3</span> <span class="title">Confidence Intervals</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.3</span> <span class="title">Exercises</span></a></div></li></ul>
 </li>
 </ul>
 </li>

sec-Set-Theory.html

@@ -62,7 +62,7 @@ window.MathJax = {
       "[pretext]/mathjaxknowl3.js"
     ],
     "paths": {
-      "pretext": "_static/pretext/js/lib"
+      "pretext": "_static/pretext/js"
     }
   },
   "startup": {
@@ -79,7 +79,7 @@ window.MathJax = {
 <meta property="og:type" content="book">
 <meta property="book:title" content="Math 1044 Notes">
 <meta property="book:author" content="Andy Eisenberg">
-<script src="_static/pretext/js/lib/jquery.min.js"></script><script src="_static/pretext/js/lib/jquery.sticky.js"></script><script src="_static/pretext/js/lib/jquery.espy.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><script src="_static/pretext/js/user_preferences.js"></script><!--** eBookCongig is necessary to configure interactive       **-->
+<script src="_static/pretext/js/jquery.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><!--** eBookCongig is necessary to configure interactive       **-->
 <!--** Runestone components to run locally in reader's browser **-->
 <!--** No external communication:                              **-->
 <!--**     log level is 0, Runestone Services are disabled     **-->
@@ -101,16 +101,16 @@ eBookConfig.allow_pairs = false;
 eBookConfig.enableScratchAC = false;
 eBookConfig.build_info = "";
 eBookConfig.python3 = null;
-eBookConfig.runestone_version = '7.11.11';
+eBookConfig.runestone_version = '7.11.13';
 eBookConfig.jobehost = '';
 eBookConfig.proxyuri_runs = '';
 eBookConfig.proxyuri_files = '';
 eBookConfig.enable_chatcodes =  false;
 </script>
 <!--*** Runestone Services ***-->
-<script src="_static/prefix-runtime.fc0e080e84d54281.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
+<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
 <link rel="stylesheet" type="text/css" href="_static/prefix-runestone.6ec5960970d8b364.css">
-<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/lib/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
+<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
 </script>
 </head>
 <body class="pretext book ignore-math">
@@ -151,6 +151,9 @@ eBookConfig.enable_chatcodes =  false;
 \DeclareMathOperator{\E}{E}
 \DeclareMathOperator{\Var}{Var}
 \DeclareMathOperator{\Cov}{Cov}
+\newcommand{\L}{\mathcal{L}}
+
+\newcommand{\est}{\widehat}
 \newcommand{\lt}{&lt;}
 \newcommand{\gt}{&gt;}
 \newcommand{\amp}{&amp;}
@@ -244,12 +247,16 @@ eBookConfig.enable_chatcodes =  false;
 <div class="toc-title-box"><a href="ch-Confidence-Intervals.html" class="internal"><span class="codenumber">4</span> <span class="title">Confidence Intervals</span></a></div>
 <ul class="structural toc-item-list">
 <li class="toc-item toc-section">
-<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Central Limit Theorem</span></a></div>
-<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
+<div class="toc-title-box"><a href="sec-Likelihood.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Likelihood</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Likelihood.html#sec-Likelihood-20" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
 </li>
 <li class="toc-item toc-section">
-<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Confidence Intervals</span></a></div>
-<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
+<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Central Limit Theorem</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.3</span> <span class="title">Confidence Intervals</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.3</span> <span class="title">Exercises</span></a></div></li></ul>
 </li>
 </ul>
 </li>

sec-Two-Sample-Tests.html

@@ -62,7 +62,7 @@ window.MathJax = {
       "[pretext]/mathjaxknowl3.js"
     ],
     "paths": {
-      "pretext": "_static/pretext/js/lib"
+      "pretext": "_static/pretext/js"
     }
   },
   "startup": {
@@ -79,7 +79,7 @@ window.MathJax = {
 <meta property="og:type" content="book">
 <meta property="book:title" content="Math 1044 Notes">
 <meta property="book:author" content="Andy Eisenberg">
-<script src="_static/pretext/js/lib/jquery.min.js"></script><script src="_static/pretext/js/lib/jquery.sticky.js"></script><script src="_static/pretext/js/lib/jquery.espy.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><script src="_static/pretext/js/user_preferences.js"></script><!--** eBookCongig is necessary to configure interactive       **-->
+<script src="_static/pretext/js/jquery.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><!--** eBookCongig is necessary to configure interactive       **-->
 <!--** Runestone components to run locally in reader's browser **-->
 <!--** No external communication:                              **-->
 <!--**     log level is 0, Runestone Services are disabled     **-->
@@ -101,16 +101,16 @@ eBookConfig.allow_pairs = false;
 eBookConfig.enableScratchAC = false;
 eBookConfig.build_info = "";
 eBookConfig.python3 = null;
-eBookConfig.runestone_version = '7.11.11';
+eBookConfig.runestone_version = '7.11.13';
 eBookConfig.jobehost = '';
 eBookConfig.proxyuri_runs = '';
 eBookConfig.proxyuri_files = '';
 eBookConfig.enable_chatcodes =  false;
 </script>
 <!--*** Runestone Services ***-->
-<script src="_static/prefix-runtime.fc0e080e84d54281.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
+<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
 <link rel="stylesheet" type="text/css" href="_static/prefix-runestone.6ec5960970d8b364.css">
-<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/lib/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
+<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
 </script>
 </head>
 <body class="pretext book ignore-math">
@@ -151,6 +151,9 @@ eBookConfig.enable_chatcodes =  false;
 \DeclareMathOperator{\E}{E}
 \DeclareMathOperator{\Var}{Var}
 \DeclareMathOperator{\Cov}{Cov}
+\newcommand{\L}{\mathcal{L}}
+
+\newcommand{\est}{\widehat}
 \newcommand{\lt}{&lt;}
 \newcommand{\gt}{&gt;}
 \newcommand{\amp}{&amp;}
@@ -244,12 +247,16 @@ eBookConfig.enable_chatcodes =  false;
 <div class="toc-title-box"><a href="ch-Confidence-Intervals.html" class="internal"><span class="codenumber">4</span> <span class="title">Confidence Intervals</span></a></div>
 <ul class="structural toc-item-list">
 <li class="toc-item toc-section">
-<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Central Limit Theorem</span></a></div>
-<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
+<div class="toc-title-box"><a href="sec-Likelihood.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Likelihood</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Likelihood.html#sec-Likelihood-20" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
 </li>
 <li class="toc-item toc-section">
-<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Confidence Intervals</span></a></div>
-<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
+<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Central Limit Theorem</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.3</span> <span class="title">Confidence Intervals</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.3</span> <span class="title">Exercises</span></a></div></li></ul>
 </li>
 </ul>
 </li>

sec-Variance.html

@@ -62,7 +62,7 @@ window.MathJax = {
       "[pretext]/mathjaxknowl3.js"
     ],
     "paths": {
-      "pretext": "_static/pretext/js/lib"
+      "pretext": "_static/pretext/js"
     }
   },
   "startup": {
@@ -79,7 +79,7 @@ window.MathJax = {
 <meta property="og:type" content="book">
 <meta property="book:title" content="Math 1044 Notes">
 <meta property="book:author" content="Andy Eisenberg">
-<script src="_static/pretext/js/lib/jquery.min.js"></script><script src="_static/pretext/js/lib/jquery.sticky.js"></script><script src="_static/pretext/js/lib/jquery.espy.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><script src="_static/pretext/js/user_preferences.js"></script><!--** eBookCongig is necessary to configure interactive       **-->
+<script src="_static/pretext/js/jquery.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><!--** eBookCongig is necessary to configure interactive       **-->
 <!--** Runestone components to run locally in reader's browser **-->
 <!--** No external communication:                              **-->
 <!--**     log level is 0, Runestone Services are disabled     **-->
@@ -101,16 +101,16 @@ eBookConfig.allow_pairs = false;
 eBookConfig.enableScratchAC = false;
 eBookConfig.build_info = "";
 eBookConfig.python3 = null;
-eBookConfig.runestone_version = '7.11.11';
+eBookConfig.runestone_version = '7.11.13';
 eBookConfig.jobehost = '';
 eBookConfig.proxyuri_runs = '';
 eBookConfig.proxyuri_files = '';
 eBookConfig.enable_chatcodes =  false;
 </script>
 <!--*** Runestone Services ***-->
-<script src="_static/prefix-runtime.fc0e080e84d54281.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
+<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
 <link rel="stylesheet" type="text/css" href="_static/prefix-runestone.6ec5960970d8b364.css">
-<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/lib/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
+<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
 </script>
 </head>
 <body class="pretext book ignore-math">
@@ -151,6 +151,9 @@ eBookConfig.enable_chatcodes =  false;
 \DeclareMathOperator{\E}{E}
 \DeclareMathOperator{\Var}{Var}
 \DeclareMathOperator{\Cov}{Cov}
+\newcommand{\L}{\mathcal{L}}
+
+\newcommand{\est}{\widehat}
 \newcommand{\lt}{&lt;}
 \newcommand{\gt}{&gt;}
 \newcommand{\amp}{&amp;}
@@ -244,12 +247,16 @@ eBookConfig.enable_chatcodes =  false;
 <div class="toc-title-box"><a href="ch-Confidence-Intervals.html" class="internal"><span class="codenumber">4</span> <span class="title">Confidence Intervals</span></a></div>
 <ul class="structural toc-item-list">
 <li class="toc-item toc-section">
-<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Central Limit Theorem</span></a></div>
-<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
+<div class="toc-title-box"><a href="sec-Likelihood.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Likelihood</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Likelihood.html#sec-Likelihood-20" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
 </li>
 <li class="toc-item toc-section">
-<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Confidence Intervals</span></a></div>
-<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
+<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Central Limit Theorem</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.3</span> <span class="title">Confidence Intervals</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.3</span> <span class="title">Exercises</span></a></div></li></ul>
 </li>
 </ul>
 </li>