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", "sec-Discrete-RVs", "sec-Continuous-RVs", "sec-Joint-Distributions"], "source/ch-Expected-Value.ptx": ["ch-Expected-Value", "sec-Expected-Value", "sec-Variance", "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"], "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"]}

_static/207.f37c7cddd9242233.js.LICENSE.txt

@@ -0,0 +1,6 @@
+/**!
+ * Sortable 1.14.0
+ * @author	RubaXa   <trash@rubaxa.org>
+ * @author	owenm    <owen23355@gmail.com>
+ * @license MIT
+ */

_static/_runestone-services.xml

@@ -1,14 +1,14 @@
 <?xml version="1.0" ?>
 <all>
 	<js type="list">
-		<item type="str">prefix-runtime.991c135ccf182bf5.bundle.js</item>
+		<item type="str">prefix-runtime.fc0e080e84d54281.bundle.js</item>
 		<item type="str">prefix-723.3e6434f80549315a.bundle.js</item>
-		<item type="str">prefix-runestone.1c010553c35c544c.bundle.js</item>
+		<item type="str">prefix-runestone.e2abc79debce15fd.bundle.js</item>
 	</js>
 	<css type="list">
 		<item type="str">prefix-723.3bccd435914aa0ff.css</item>
-		<item type="str">prefix-runestone.677a75a9120449ff.css</item>
+		<item type="str">prefix-runestone.6ec5960970d8b364.css</item>
 	</css>
 	<cdn-url type="str">https://runestone.academy/cdn/runestone/</cdn-url>
-	<version type="str">7.11.8</version>
+	<version type="str">7.11.11</version>
 </all>

_static/prefix-runestone.e2abc79debce15fd.bundle.js.LICENSE.txt

@@ -0,0 +1,83 @@
+/*!
+ * BIDI embedding support for jQuery.i18n
+ *
+ * Copyright (C) 2015, David Chan
+ *
+ * This code is dual licensed GPLv2 or later and MIT. You don't have to do
+ * anything special to choose one license or the other and you don't have to
+ * notify anyone which license you are using. You are free to use this code
+ * in commercial projects as long as the copyright header is left intact.
+ * See files GPL-LICENSE and MIT-LICENSE for details.
+ *
+ * @licence GNU General Public Licence 2.0 or later
+ * @licence MIT License
+ */
+
+/*!
+ * jQuery Internationalization library
+ *
+ * Copyright (C) 2011-2013 Santhosh Thottingal, Neil Kandalgaonkar
+ *
+ * jquery.i18n is dual licensed GPLv2 or later and MIT. You don't have to do
+ * anything special to choose one license or the other and you don't have to
+ * notify anyone which license you are using. You are free to use
+ * UniversalLanguageSelector in commercial projects as long as the copyright
+ * header is left intact. See files GPL-LICENSE and MIT-LICENSE for details.
+ *
+ * @licence GNU General Public Licence 2.0 or later
+ * @licence MIT License
+ */
+
+/*!
+ * jQuery Internationalization library
+ *
+ * Copyright (C) 2012 Santhosh Thottingal
+ *
+ * jquery.i18n is dual licensed GPLv2 or later and MIT. You don't have to do
+ * anything special to choose one license or the other and you don't have to
+ * notify anyone which license you are using. You are free to use
+ * UniversalLanguageSelector in commercial projects as long as the copyright
+ * header is left intact. See files GPL-LICENSE and MIT-LICENSE for details.
+ *
+ * @licence GNU General Public Licence 2.0 or later
+ * @licence MIT License
+ */
+
+/*!
+ * jQuery Internationalization library
+ *
+ * Copyright (C) 2012 Santhosh Thottingal
+ *
+ * jquery.i18n is dual licensed GPLv2 or later and MIT. You don't have to do anything special to
+ * choose one license or the other and you don't have to notify anyone which license you are using.
+ * You are free to use UniversalLanguageSelector in commercial projects as long as the copyright
+ * header is left intact. See files GPL-LICENSE and MIT-LICENSE for details.
+ *
+ * @licence GNU General Public Licence 2.0 or later
+ * @licence MIT License
+ */
+
+/*!
+ * jQuery Internationalization library - Message Store
+ *
+ * Copyright (C) 2012 Santhosh Thottingal
+ *
+ * jquery.i18n is dual licensed GPLv2 or later and MIT. You don't have to do anything special to
+ * choose one license or the other and you don't have to notify anyone which license you are using.
+ * You are free to use UniversalLanguageSelector in commercial projects as long as the copyright
+ * header is left intact. See files GPL-LICENSE and MIT-LICENSE for details.
+ *
+ * @licence GNU General Public Licence 2.0 or later
+ * @licence MIT License
+ */
+
+/*!
+ * jQuery idleTimer plugin
+ * version 0.9.100511
+ * by Paul Irish.
+ *   http://github.com/paulirish/yui-misc/tree/
+ * MIT license
+
+ * adapted from YUI idle timer by nzakas:
+ *   http://github.com/nzakas/yui-misc/
+*/

_static/webpack_static_imports.json

@@ -1 +1 @@
-{"js":["prefix-runtime.991c135ccf182bf5.bundle.js","prefix-723.3e6434f80549315a.bundle.js","prefix-runestone.1c010553c35c544c.bundle.js"],"css":["prefix-723.3bccd435914aa0ff.css","prefix-runestone.677a75a9120449ff.css"]}
+{"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"]}

_static/webpack_static_imports.xml

@@ -1,14 +1,14 @@
 <?xml version="1.0" ?>
 <all>
 	<js type="list">
-		<item type="str">prefix-runtime.991c135ccf182bf5.bundle.js</item>
+		<item type="str">prefix-runtime.fc0e080e84d54281.bundle.js</item>
 		<item type="str">prefix-723.3e6434f80549315a.bundle.js</item>
-		<item type="str">prefix-runestone.1c010553c35c544c.bundle.js</item>
+		<item type="str">prefix-runestone.e2abc79debce15fd.bundle.js</item>
 	</js>
 	<css type="list">
 		<item type="str">prefix-723.3bccd435914aa0ff.css</item>
-		<item type="str">prefix-runestone.677a75a9120449ff.css</item>
+		<item type="str">prefix-runestone.6ec5960970d8b364.css</item>
 	</css>
 	<cdn-url type="str">https://runestone.academy/cdn/runestone/</cdn-url>
-	<version type="str">7.11.8</version>
+	<version type="str">7.11.11</version>
 </all>

backmatter-2.html

@@ -101,15 +101,15 @@ eBookConfig.allow_pairs = false;
 eBookConfig.enableScratchAC = false;
 eBookConfig.build_info = "";
 eBookConfig.python3 = null;
-eBookConfig.runestone_version = '7.11.8';
+eBookConfig.runestone_version = '7.11.11';
 eBookConfig.jobehost = '';
 eBookConfig.proxyuri_runs = '';
 eBookConfig.proxyuri_files = '';
 eBookConfig.enable_chatcodes =  false;
 </script>
 <!--*** Runestone Services ***-->
-<script src="_static/prefix-runtime.991c135ccf182bf5.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.1c010553c35c544c.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
+<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">
-<link rel="stylesheet" type="text/css" href="_static/prefix-runestone.677a75a9120449ff.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>
 </head>

backmatter.html

@@ -101,15 +101,15 @@ eBookConfig.allow_pairs = false;
 eBookConfig.enableScratchAC = false;
 eBookConfig.build_info = "";
 eBookConfig.python3 = null;
-eBookConfig.runestone_version = '7.11.8';
+eBookConfig.runestone_version = '7.11.11';
 eBookConfig.jobehost = '';
 eBookConfig.proxyuri_runs = '';
 eBookConfig.proxyuri_files = '';
 eBookConfig.enable_chatcodes =  false;
 </script>
 <!--*** Runestone Services ***-->
-<script src="_static/prefix-runtime.991c135ccf182bf5.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.1c010553c35c544c.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
+<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">
-<link rel="stylesheet" type="text/css" href="_static/prefix-runestone.677a75a9120449ff.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>
 </head>

ch-Confidence-Intervals.html

@@ -101,15 +101,15 @@ eBookConfig.allow_pairs = false;
 eBookConfig.enableScratchAC = false;
 eBookConfig.build_info = "";
 eBookConfig.python3 = null;
-eBookConfig.runestone_version = '7.11.8';
+eBookConfig.runestone_version = '7.11.11';
 eBookConfig.jobehost = '';
 eBookConfig.proxyuri_runs = '';
 eBookConfig.proxyuri_files = '';
 eBookConfig.enable_chatcodes =  false;
 </script>
 <!--*** Runestone Services ***-->
-<script src="_static/prefix-runtime.991c135ccf182bf5.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.1c010553c35c544c.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
+<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">
-<link rel="stylesheet" type="text/css" href="_static/prefix-runestone.677a75a9120449ff.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>
 </head>

ch-Expected-Value.html

@@ -101,15 +101,15 @@ eBookConfig.allow_pairs = false;
 eBookConfig.enableScratchAC = false;
 eBookConfig.build_info = "";
 eBookConfig.python3 = null;
-eBookConfig.runestone_version = '7.11.8';
+eBookConfig.runestone_version = '7.11.11';
 eBookConfig.jobehost = '';
 eBookConfig.proxyuri_runs = '';
 eBookConfig.proxyuri_files = '';
 eBookConfig.enable_chatcodes =  false;
 </script>
 <!--*** Runestone Services ***-->
-<script src="_static/prefix-runtime.991c135ccf182bf5.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.1c010553c35c544c.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
+<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">
-<link rel="stylesheet" type="text/css" href="_static/prefix-runestone.677a75a9120449ff.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>
 </head>
@@ -292,7 +292,7 @@ eBookConfig.enable_chatcodes =  false;
 <main class="ptx-main"><div id="ptx-content" class="ptx-content"><section class="chapter" id="ch-Expected-Value"><h2 class="heading">
 <span class="type">Chapter</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">3</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Expected Value and Variance</span>
 </h2>
-<section class="introduction" id="ch-Expected-Value-2"><div class="para" id="ch-Expected-Value-2-1"><div class="autopermalink" data-description="Paragraph"><a href="#ch-Expected-Value-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div></div></section><nav class="summary-links"><ul>
+<nav class="summary-links"><ul>
 <li><a href="sec-Expected-Value.html" class="internal"><span class="codenumber">3.1</span> <span class="title">Expected Value</span></a></li>
 <li><a href="sec-Variance.html" class="internal"><span class="codenumber">3.2</span> <span class="title">Variance</span></a></li>
 <li><a href="sec-Covariance.html" class="internal"><span class="codenumber">3.3</span> <span class="title">Covariance</span></a></li>

ch-Hypothesis-Testing.html

@@ -101,15 +101,15 @@ eBookConfig.allow_pairs = false;
 eBookConfig.enableScratchAC = false;
 eBookConfig.build_info = "";
 eBookConfig.python3 = null;
-eBookConfig.runestone_version = '7.11.8';
+eBookConfig.runestone_version = '7.11.11';
 eBookConfig.jobehost = '';
 eBookConfig.proxyuri_runs = '';
 eBookConfig.proxyuri_files = '';
 eBookConfig.enable_chatcodes =  false;
 </script>
 <!--*** Runestone Services ***-->
-<script src="_static/prefix-runtime.991c135ccf182bf5.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.1c010553c35c544c.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
+<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">
-<link rel="stylesheet" type="text/css" href="_static/prefix-runestone.677a75a9120449ff.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>
 </head>

ch-Introduction.html

@@ -101,15 +101,15 @@ eBookConfig.allow_pairs = false;
 eBookConfig.enableScratchAC = false;
 eBookConfig.build_info = "";
 eBookConfig.python3 = null;
-eBookConfig.runestone_version = '7.11.8';
+eBookConfig.runestone_version = '7.11.11';
 eBookConfig.jobehost = '';
 eBookConfig.proxyuri_runs = '';
 eBookConfig.proxyuri_files = '';
 eBookConfig.enable_chatcodes =  false;
 </script>
 <!--*** Runestone Services ***-->
-<script src="_static/prefix-runtime.991c135ccf182bf5.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.1c010553c35c544c.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
+<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">
-<link rel="stylesheet" type="text/css" href="_static/prefix-runestone.677a75a9120449ff.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>
 </head>

ch-Linear-Regression.html

@@ -101,15 +101,15 @@ eBookConfig.allow_pairs = false;
 eBookConfig.enableScratchAC = false;
 eBookConfig.build_info = "";
 eBookConfig.python3 = null;
-eBookConfig.runestone_version = '7.11.8';
+eBookConfig.runestone_version = '7.11.11';
 eBookConfig.jobehost = '';
 eBookConfig.proxyuri_runs = '';
 eBookConfig.proxyuri_files = '';
 eBookConfig.enable_chatcodes =  false;
 </script>
 <!--*** Runestone Services ***-->
-<script src="_static/prefix-runtime.991c135ccf182bf5.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.1c010553c35c544c.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
+<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">
-<link rel="stylesheet" type="text/css" href="_static/prefix-runestone.677a75a9120449ff.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>
 </head>

ch-Probability.html

@@ -101,15 +101,15 @@ eBookConfig.allow_pairs = false;
 eBookConfig.enableScratchAC = false;
 eBookConfig.build_info = "";
 eBookConfig.python3 = null;
-eBookConfig.runestone_version = '7.11.8';
+eBookConfig.runestone_version = '7.11.11';
 eBookConfig.jobehost = '';
 eBookConfig.proxyuri_runs = '';
 eBookConfig.proxyuri_files = '';
 eBookConfig.enable_chatcodes =  false;
 </script>
 <!--*** Runestone Services ***-->
-<script src="_static/prefix-runtime.991c135ccf182bf5.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.1c010553c35c544c.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
+<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">
-<link rel="stylesheet" type="text/css" href="_static/prefix-runestone.677a75a9120449ff.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>
 </head>

ch-Random-Variables.html

@@ -101,15 +101,15 @@ eBookConfig.allow_pairs = false;
 eBookConfig.enableScratchAC = false;
 eBookConfig.build_info = "";
 eBookConfig.python3 = null;
-eBookConfig.runestone_version = '7.11.8';
+eBookConfig.runestone_version = '7.11.11';
 eBookConfig.jobehost = '';
 eBookConfig.proxyuri_runs = '';
 eBookConfig.proxyuri_files = '';
 eBookConfig.enable_chatcodes =  false;
 </script>
 <!--*** Runestone Services ***-->
-<script src="_static/prefix-runtime.991c135ccf182bf5.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.1c010553c35c544c.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
+<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">
-<link rel="stylesheet" type="text/css" href="_static/prefix-runestone.677a75a9120449ff.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>
 </head>

front-colophon.html

@@ -101,15 +101,15 @@ eBookConfig.allow_pairs = false;
 eBookConfig.enableScratchAC = false;
 eBookConfig.build_info = "";
 eBookConfig.python3 = null;
-eBookConfig.runestone_version = '7.11.8';
+eBookConfig.runestone_version = '7.11.11';
 eBookConfig.jobehost = '';
 eBookConfig.proxyuri_runs = '';
 eBookConfig.proxyuri_files = '';
 eBookConfig.enable_chatcodes =  false;
 </script>
 <!--*** Runestone Services ***-->
-<script src="_static/prefix-runtime.991c135ccf182bf5.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.1c010553c35c544c.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
+<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">
-<link rel="stylesheet" type="text/css" href="_static/prefix-runestone.677a75a9120449ff.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>
 </head>

frontmatter.html

@@ -101,15 +101,15 @@ eBookConfig.allow_pairs = false;
 eBookConfig.enableScratchAC = false;
 eBookConfig.build_info = "";
 eBookConfig.python3 = null;
-eBookConfig.runestone_version = '7.11.8';
+eBookConfig.runestone_version = '7.11.11';
 eBookConfig.jobehost = '';
 eBookConfig.proxyuri_runs = '';
 eBookConfig.proxyuri_files = '';
 eBookConfig.enable_chatcodes =  false;
 </script>
 <!--*** Runestone Services ***-->
-<script src="_static/prefix-runtime.991c135ccf182bf5.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.1c010553c35c544c.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
+<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">
-<link rel="stylesheet" type="text/css" href="_static/prefix-runestone.677a75a9120449ff.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>
 </head>
@@ -294,7 +294,7 @@ 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 11, 2026</div>
+<div class="date">January 29, 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">
 <a class="previous-button button" href="my-great-book.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="front-colophon.html" title="Next"><span class="name">Next</span><span class="icon material-symbols-outlined" aria-hidden="true">&#xe5cc;</span></a>

index.html

@@ -2,7 +2,7 @@
 <html>
 <!--********************************************-->
 <!--*       Generated from PreTeXt source      *-->
-<!--*       on 2026-01-11T14:41:58-05:00       *-->
+<!--*       on 2026-01-29T06:34:50-05:00       *-->
 <!--*   A recent stable commit (2022-07-01):   *-->
 <!--* 6c761d3dba23af92cba35001c852aac04ae99a5f *-->
 <!--*                                          *-->

my-great-book.html

@@ -101,15 +101,15 @@ eBookConfig.allow_pairs = false;
 eBookConfig.enableScratchAC = false;
 eBookConfig.build_info = "";
 eBookConfig.python3 = null;
-eBookConfig.runestone_version = '7.11.8';
+eBookConfig.runestone_version = '7.11.11';
 eBookConfig.jobehost = '';
 eBookConfig.proxyuri_runs = '';
 eBookConfig.proxyuri_files = '';
 eBookConfig.enable_chatcodes =  false;
 </script>
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-<script src="_static/prefix-runtime.991c135ccf182bf5.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.1c010553c35c544c.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
+<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">
-<link rel="stylesheet" type="text/css" href="_static/prefix-runestone.677a75a9120449ff.css">
+<link rel="stylesheet" type="text/css" href="_static/prefix-runestone.6ec5960970d8b364.css">
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 </script>
 </head>

sec-CLT.html

@@ -101,15 +101,15 @@ eBookConfig.allow_pairs = false;
 eBookConfig.enableScratchAC = false;
 eBookConfig.build_info = "";
 eBookConfig.python3 = null;
-eBookConfig.runestone_version = '7.11.8';
+eBookConfig.runestone_version = '7.11.11';
 eBookConfig.jobehost = '';
 eBookConfig.proxyuri_runs = '';
 eBookConfig.proxyuri_files = '';
 eBookConfig.enable_chatcodes =  false;
 </script>
 <!--*** Runestone Services ***-->
-<script src="_static/prefix-runtime.991c135ccf182bf5.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.1c010553c35c544c.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
+<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">
-<link rel="stylesheet" type="text/css" href="_static/prefix-runestone.677a75a9120449ff.css">
+<link rel="stylesheet" type="text/css" href="_static/prefix-runestone.6ec5960970d8b364.css">
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 </script>
 </head>

sec-Chi-Squared.html

@@ -101,15 +101,15 @@ eBookConfig.allow_pairs = false;
 eBookConfig.enableScratchAC = false;
 eBookConfig.build_info = "";
 eBookConfig.python3 = null;
-eBookConfig.runestone_version = '7.11.8';
+eBookConfig.runestone_version = '7.11.11';
 eBookConfig.jobehost = '';
 eBookConfig.proxyuri_runs = '';
 eBookConfig.proxyuri_files = '';
 eBookConfig.enable_chatcodes =  false;
 </script>
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+<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">
-<link rel="stylesheet" type="text/css" href="_static/prefix-runestone.677a75a9120449ff.css">
+<link rel="stylesheet" type="text/css" href="_static/prefix-runestone.6ec5960970d8b364.css">
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 </script>
 </head>

sec-Conditional-Probability.html

@@ -101,15 +101,15 @@ eBookConfig.allow_pairs = false;
 eBookConfig.enableScratchAC = false;
 eBookConfig.build_info = "";
 eBookConfig.python3 = null;
-eBookConfig.runestone_version = '7.11.8';
+eBookConfig.runestone_version = '7.11.11';
 eBookConfig.jobehost = '';
 eBookConfig.proxyuri_runs = '';
 eBookConfig.proxyuri_files = '';
 eBookConfig.enable_chatcodes =  false;
 </script>
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-<script src="_static/prefix-runtime.991c135ccf182bf5.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.1c010553c35c544c.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
+<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">
-<link rel="stylesheet" type="text/css" href="_static/prefix-runestone.677a75a9120449ff.css">
+<link rel="stylesheet" type="text/css" href="_static/prefix-runestone.6ec5960970d8b364.css">
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 </script>
 </head>

sec-Confidence-Intervals.html

@@ -101,15 +101,15 @@ eBookConfig.allow_pairs = false;
 eBookConfig.enableScratchAC = false;
 eBookConfig.build_info = "";
 eBookConfig.python3 = null;
-eBookConfig.runestone_version = '7.11.8';
+eBookConfig.runestone_version = '7.11.11';
 eBookConfig.jobehost = '';
 eBookConfig.proxyuri_runs = '';
 eBookConfig.proxyuri_files = '';
 eBookConfig.enable_chatcodes =  false;
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-<script src="_static/prefix-runtime.991c135ccf182bf5.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.1c010553c35c544c.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
+<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">
-<link rel="stylesheet" type="text/css" href="_static/prefix-runestone.677a75a9120449ff.css">
+<link rel="stylesheet" type="text/css" href="_static/prefix-runestone.6ec5960970d8b364.css">
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 </script>
 </head>

sec-Continuous-RVs.html

@@ -101,15 +101,15 @@ eBookConfig.allow_pairs = false;
 eBookConfig.enableScratchAC = false;
 eBookConfig.build_info = "";
 eBookConfig.python3 = null;
-eBookConfig.runestone_version = '7.11.8';
+eBookConfig.runestone_version = '7.11.11';
 eBookConfig.jobehost = '';
 eBookConfig.proxyuri_runs = '';
 eBookConfig.proxyuri_files = '';
 eBookConfig.enable_chatcodes =  false;
 </script>
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+<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">
-<link rel="stylesheet" type="text/css" href="_static/prefix-runestone.677a75a9120449ff.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>
 </head>
@@ -531,21 +531,54 @@ f(x; \mu, \sigma^2) = \frac{1}{\sqrt{2\pi \sigma^2}} e^{\frac{-(x-\mu)^2}{2\sigm
 <span class="type">Exercises</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">2.2.5</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Exercises</span>
 </h3>
 <article class="exercise exercise-like" id="exercises-Continuous-RVs-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-Continuous-RVs-1-1-1">A continuous random variable <span class="process-math">\(X\)</span> taking values in <span class="process-math">\([1, 4]\)</span> has p.d.f. <span class="process-math">\(f(x) = k(x - \sqrt{x})\)</span> for some constant <span class="process-math">\(k\text{.}\)</span> What is the value of <span class="process-math">\(k\text{?}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-Continuous-RVs-1-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+<div class="introduction" id="exercises-Continuous-RVs-1-1"><div class="para" id="exercises-Continuous-RVs-1-1-1">A continuous random variable <span class="process-math">\(X\)</span> taking values in <span class="process-math">\([1, 4]\)</span> has p.d.f. <span class="process-math">\(f(x) = k(x - \sqrt{x})\)</span> for some constant <span class="process-math">\(k\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-Continuous-RVs-1-1-1" 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-Continuous-RVs-1-2"><h5 class="heading"><span class="codenumber">(a)</span></h5>
+<div class="para" id="exercises-Continuous-RVs-1-2-1-1">What is the value of <span class="process-math">\(k\text{?}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-Continuous-RVs-1-2-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
 </div>
-<div class="autopermalink" data-description="Exercise 2.2.5.1"><a href="#exercises-Continuous-RVs-1" title="Copy heading and permalink for Exercise 2.2.5.1" aria-label="Copy heading and permalink for Exercise 2.2.5.1">🔗</a></div></article><article class="exercise exercise-like" id="exercises-Continuous-RVs-2"><h4 class="heading"><span class="codenumber">2<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
+<div class="solutions"><details id="exercises-Continuous-RVs-1-2-2" 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="exercises-Continuous-RVs-1-2-2-1">
+<span class="process-math">\(k = \frac{6}{17}.\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-Continuous-RVs-1-2-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Answer 2.2.5.1.a.1"><a href="#exercises-Continuous-RVs-1-2-2" title="Copy heading and permalink for Answer 2.2.5.1.a.1" aria-label="Copy heading and permalink for Answer 2.2.5.1.a.1">🔗</a></div>
+</div></details></div>
+<div class="autopermalink" data-description="Task 2.2.5.1.a"><a href="#exercises-Continuous-RVs-1-2" title="Copy heading and permalink for Task 2.2.5.1.a" aria-label="Copy heading and permalink for Task 2.2.5.1.a">🔗</a></div></article><article class="task exercise-like" id="exercises-Continuous-RVs-1-3"><h5 class="heading"><span class="codenumber">(b)</span></h5>
+<div class="para" id="exercises-Continuous-RVs-1-3-1-1">Find <span class="process-math">\(\Pr(2 \leq X \leq 3).\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-Continuous-RVs-1-3-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="solutions"><details id="exercises-Continuous-RVs-1-3-2" 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="exercises-Continuous-RVs-1-3-2-1">
+<span class="process-math">\(\Pr(2 \leq X \leq 3) \approx 0.325\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-Continuous-RVs-1-3-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Answer 2.2.5.1.b.1"><a href="#exercises-Continuous-RVs-1-3-2" title="Copy heading and permalink for Answer 2.2.5.1.b.1" aria-label="Copy heading and permalink for Answer 2.2.5.1.b.1">🔗</a></div>
+</div></details></div>
+<div class="autopermalink" data-description="Task 2.2.5.1.b"><a href="#exercises-Continuous-RVs-1-3" title="Copy heading and permalink for Task 2.2.5.1.b" aria-label="Copy heading and permalink for Task 2.2.5.1.b">🔗</a></div></article><div class="autopermalink" data-description="Exercise 2.2.5.1"><a href="#exercises-Continuous-RVs-1" title="Copy heading and permalink for Exercise 2.2.5.1" aria-label="Copy heading and permalink for Exercise 2.2.5.1">🔗</a></div></article><article class="exercise exercise-like" id="exercises-Continuous-RVs-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="exercises-Continuous-RVs-2-1-1">A continuous random variable <span class="process-math">\(X\)</span> taking values in <span class="process-math">\([1, 2]\)</span> has p.d.f. <span class="process-math">\(\displaystyle{f(x) = \frac{1}{2}\left(\frac{1}{x^2} + x\right)}\text{.}\)</span> Find the c.d.f. <span class="process-math">\(F(x)\text{.}\)</span> Use your c.d.f. to find <span class="process-math">\(\Pr\left(1 \leq X \leq \frac{3}{2}\right)\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-Continuous-RVs-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="exercises-Continuous-RVs-2-2" 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="exercises-Continuous-RVs-2-2-1">
+<span class="process-math">\(\frac{1}{2}\left(\frac{x^2}{2} - \frac{1}{x}\right) + \frac{1}{4}\text{.}\)</span> <span class="process-math">\(\Pr\left(1 \leq X \leq \frac{3}{2}\right) \approx 0.479.\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-Continuous-RVs-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="Answer 2.2.5.2.1"><a href="#exercises-Continuous-RVs-2-2" title="Copy heading and permalink for Answer 2.2.5.2.1" aria-label="Copy heading and permalink for Answer 2.2.5.2.1">🔗</a></div>
+</div></details></div>
 <div class="autopermalink" data-description="Exercise 2.2.5.2"><a href="#exercises-Continuous-RVs-2" title="Copy heading and permalink for Exercise 2.2.5.2" aria-label="Copy heading and permalink for Exercise 2.2.5.2">🔗</a></div></article><article class="exercise exercise-like" id="exercises-Continuous-RVs-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-Continuous-RVs-3-1-1">A continuous random variable <span class="process-math">\(X\)</span> taking values in <span class="process-math">\([2, 3]\)</span> has c.d.f. <span class="process-math">\(F(x) = \frac{x^3}{3} - x^2 + 4\text{.}\)</span> Find the p.d.f. <span class="process-math">\(f(x)\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-Continuous-RVs-3-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
 </div>
+<div class="solutions"><details id="exercises-Continuous-RVs-3-2" 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="exercises-Continuous-RVs-3-2-1">
+<span class="process-math">\(f(x) = x^2 - 2x.\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-Continuous-RVs-3-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Answer 2.2.5.3.1"><a href="#exercises-Continuous-RVs-3-2" title="Copy heading and permalink for Answer 2.2.5.3.1" aria-label="Copy heading and permalink for Answer 2.2.5.3.1">🔗</a></div>
+</div></details></div>
 <div class="autopermalink" data-description="Exercise 2.2.5.3"><a href="#exercises-Continuous-RVs-3" title="Copy heading and permalink for Exercise 2.2.5.3" aria-label="Copy heading and permalink for Exercise 2.2.5.3">🔗</a></div></article><article class="exercise exercise-like" id="exercises-Continuous-RVs-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-Continuous-RVs-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="#exercises-Continuous-RVs-4-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+<div class="para" id="exercises-Continuous-RVs-4-1-1">Let <span class="process-math">\(T \sim \Exp(3)\text{.}\)</span> Find <span class="process-math">\(\Pr(1 \leq T \leq 3)\)</span> and <span class="process-math">\(\Pr(T \geq 0.5)\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-Continuous-RVs-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 2.2.5.4"><a href="#exercises-Continuous-RVs-4" title="Copy heading and permalink for Exercise 2.2.5.4" aria-label="Copy heading and permalink for Exercise 2.2.5.4">🔗</a></div></article><article class="exercise exercise-like" id="exercises-Continuous-RVs-5"><h4 class="heading"><span class="codenumber">5<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
+<div class="solutions"><details id="exercises-Continuous-RVs-4-2" 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="exercises-Continuous-RVs-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="#exercises-Continuous-RVs-5-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+<div class="para" id="exercises-Continuous-RVs-4-2-1">
+<span class="process-math">\(\Pr(1 \leq T \leq 3) \approx 0.050\text{.}\)</span> <span class="process-math">\(\Pr(T \geq 0.5) \approx 0.223\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-Continuous-RVs-4-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
 </div>
-<div class="autopermalink" data-description="Exercise 2.2.5.5"><a href="#exercises-Continuous-RVs-5" title="Copy heading and permalink for Exercise 2.2.5.5" aria-label="Copy heading and permalink for Exercise 2.2.5.5">🔗</a></div></article><div class="autopermalink" data-description="Exercises 2.2.5"><a href="#exercises-Continuous-RVs" title="Copy heading and permalink for Exercises 2.2.5" aria-label="Copy heading and permalink for Exercises 2.2.5">🔗</a></div></section><div class="autopermalink" data-description="Section 2.2: Continuous Random Variables"><a href="#sec-Continuous-RVs" title="Copy heading and permalink for Section 2.2: Continuous Random Variables" aria-label="Copy heading and permalink for Section 2.2: Continuous Random Variables">🔗</a></div></section></div>
+<div class="autopermalink" data-description="Answer 2.2.5.4.1"><a href="#exercises-Continuous-RVs-4-2" title="Copy heading and permalink for Answer 2.2.5.4.1" aria-label="Copy heading and permalink for Answer 2.2.5.4.1">🔗</a></div>
+</div></details></div>
+<div class="autopermalink" data-description="Exercise 2.2.5.4"><a href="#exercises-Continuous-RVs-4" title="Copy heading and permalink for Exercise 2.2.5.4" aria-label="Copy heading and permalink for Exercise 2.2.5.4">🔗</a></div></article><div class="autopermalink" data-description="Exercises 2.2.5"><a href="#exercises-Continuous-RVs" title="Copy heading and permalink for Exercises 2.2.5" aria-label="Copy heading and permalink for Exercises 2.2.5">🔗</a></div></section><div class="autopermalink" data-description="Section 2.2: Continuous Random Variables"><a href="#sec-Continuous-RVs" title="Copy heading and permalink for Section 2.2: Continuous Random Variables" aria-label="Copy heading and permalink for Section 2.2: Continuous Random Variables">🔗</a></div></section></div>
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sec-Correlation.html

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sec-Covariance.html

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sec-Discrete-RVs.html

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@@ -511,27 +511,67 @@ p(k; \lambda, t) = \frac{(\lambda t)^k}{k!} e^{-\lambda t}.
 <span class="type">Exercises</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">2.1.5</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Exercises</span>
 </h3>
 <article class="exercise exercise-like" id="exercises-Discrete-RVs-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-Discrete-RVs-1-1-1">We flip a coin with unknown bias 100 times and observe 43 heads. What is the maximum likelihood estimation for the probability of the coin coming up heads?<div class="autopermalink" data-description="Paragraph"><a href="#exercises-Discrete-RVs-1-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+<div class="para" id="exercises-Discrete-RVs-1-1-1">An experiment consists of flipping a biased coin 20 times. If the coin comes up heads with probability <span class="process-math">\(p = 0.3\text{,}\)</span> find the probability of seeing 5 heads. Find the probability of seeing up to (and including) 3 heads.<div class="autopermalink" data-description="Paragraph"><a href="#exercises-Discrete-RVs-1-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
 </div>
+<div class="solutions"><details id="exercises-Discrete-RVs-1-2" 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="exercises-Discrete-RVs-1-2-1">
+<div class="para">Let <span class="process-math">\(S\)</span> be the number of heads. Then <span class="process-math">\(S \sim \Bin(20, 0.3)\text{,}\)</span> so:</div>
+<div class="displaymath process-math" id="exercises-Discrete-RVs-1-2-1-3">
+\begin{align*}
+\Pr(S = 5) \amp = {20 \choose 5} (0.3)^5 (0.7)^{20 - 5} \\
+\amp = \frac{20!}{(5!)(15!)} (0.3)^5 (0.7)^{15} \\
+\amp = \frac{20 \times 19 \times 18 \times 17 \times 16}{5 \times 4 \times 3 \times 2 \times 1} (0.3)^5 (0.7)^{15} \\
+\amp = (19 \times 3 \times 17 \times 16) (0.3)^5 (0.7)^{15} \\
+\amp \approx 0.179 
+\end{align*}
+</div>
+<div class="autopermalink" data-description="Paragraph"><a href="#exercises-Discrete-RVs-1-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Solution 2.1.5.1.1"><a href="#exercises-Discrete-RVs-1-2" title="Copy heading and permalink for Solution 2.1.5.1.1" aria-label="Copy heading and permalink for Solution 2.1.5.1.1">🔗</a></div>
+</div></details></div>
 <div class="autopermalink" data-description="Exercise 2.1.5.1"><a href="#exercises-Discrete-RVs-1" title="Copy heading and permalink for Exercise 2.1.5.1" aria-label="Copy heading and permalink for Exercise 2.1.5.1">🔗</a></div></article><article class="exercise exercise-like" id="exercises-Discrete-RVs-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="exercises-Discrete-RVs-2-1-1">An experiment consists of flipping a biased coin 20 times. If the coin comes up heads with probability <span class="process-math">\(p = 0.3\text{,}\)</span> find the probability of seeing 5 heads. Find the probability of seeing up to (and including) 3 heads.<div class="autopermalink" data-description="Paragraph"><a href="#exercises-Discrete-RVs-2-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+<div class="introduction" id="exercises-Discrete-RVs-2-1"><div class="para" id="exercises-Discrete-RVs-2-1-1">An experiment consists of flipping a coin repeatedly until we first see heads.<div class="autopermalink" data-description="Paragraph"><a href="#exercises-Discrete-RVs-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-Discrete-RVs-2-2"><h5 class="heading"><span class="codenumber">(a)</span></h5>
+<div class="para" id="exercises-Discrete-RVs-2-2-1-1">If the coin comes up heads with probability 0.4, what is the probability we’ll see our first heads within three flips? What about precisely on the third flip?<div class="autopermalink" data-description="Paragraph"><a href="#exercises-Discrete-RVs-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="Exercise 2.1.5.2"><a href="#exercises-Discrete-RVs-2" title="Copy heading and permalink for Exercise 2.1.5.2" aria-label="Copy heading and permalink for Exercise 2.1.5.2">🔗</a></div></article><article class="exercise exercise-like" id="exercises-Discrete-RVs-3"><h4 class="heading"><span class="codenumber">3<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
+<div class="solutions"><details id="exercises-Discrete-RVs-2-2-2" 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" id="exercises-Discrete-RVs-3-1-1">An experiment consists of flipping a coin repeatedly until we first see heads.<div class="autopermalink" data-description="Paragraph"><a href="#exercises-Discrete-RVs-3-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+<div class="para logical" id="exercises-Discrete-RVs-2-2-2-1">
+<div class="para">Let <span class="process-math">\(T\)</span> be the number of flips until we see heads. Then <span class="process-math">\(T\)</span> is geometric with parameter <span class="process-math">\(p = 0.4\text{,}\)</span> so:</div>
+<div class="displaymath process-math" id="exercises-Discrete-RVs-2-2-2-1-4">
+\begin{align*}
+\Pr(T = k) \amp = (1-0.4)^{k-1}(0.4) = 0.6^{k-1} \cdot 0.4 
+\end{align*}
 </div>
-<div class="autopermalink" data-description="Exercise 2.1.5.3"><a href="#exercises-Discrete-RVs-3" title="Copy heading and permalink for Exercise 2.1.5.3" aria-label="Copy heading and permalink for Exercise 2.1.5.3">🔗</a></div></article><article class="exercise exercise-like" id="exercises-Discrete-RVs-4"><h4 class="heading"><span class="codenumber">4<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
+<div class="autopermalink" data-description="Paragraph"><a href="#exercises-Discrete-RVs-2-2-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
-<div class="para" id="exercises-Discrete-RVs-4-1-1">If the coin comes up heads with probability 0.4, what is the probability we’ll see our first heads within three flips? What about precisely on the third flip?<div class="autopermalink" data-description="Paragraph"><a href="#exercises-Discrete-RVs-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 2.1.5.4"><a href="#exercises-Discrete-RVs-4" title="Copy heading and permalink for Exercise 2.1.5.4" aria-label="Copy heading and permalink for Exercise 2.1.5.4">🔗</a></div></article><article class="exercise exercise-like" id="exercises-Discrete-RVs-5"><h4 class="heading"><span class="codenumber">5<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
+<div class="autopermalink" data-description="Solution 2.1.5.2.a.1"><a href="#exercises-Discrete-RVs-2-2-2" title="Copy heading and permalink for Solution 2.1.5.2.a.1" aria-label="Copy heading and permalink for Solution 2.1.5.2.a.1">🔗</a></div>
-<div class="para" id="exercises-Discrete-RVs-5-1-1">Suppose the 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="#exercises-Discrete-RVs-5-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div></details></div>
+<div class="autopermalink" data-description="Task 2.1.5.2.a"><a href="#exercises-Discrete-RVs-2-2" title="Copy heading and permalink for Task 2.1.5.2.a" aria-label="Copy heading and permalink for Task 2.1.5.2.a">🔗</a></div></article><article class="task exercise-like" id="exercises-Discrete-RVs-2-3"><h5 class="heading"><span class="codenumber">(b)</span></h5>
+<div class="para" id="exercises-Discrete-RVs-2-3-1-1">Which flip has the highest chance of being the first flip to come up heads?<div class="autopermalink" data-description="Paragraph"><a href="#exercises-Discrete-RVs-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="Exercise 2.1.5.5"><a href="#exercises-Discrete-RVs-5" title="Copy heading and permalink for Exercise 2.1.5.5" aria-label="Copy heading and permalink for Exercise 2.1.5.5">🔗</a></div></article><article class="exercise exercise-like" id="exercises-Discrete-RVs-6"><h4 class="heading"><span class="codenumber">6<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
+<div class="solutions"><details id="exercises-Discrete-RVs-2-3-2" 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" id="exercises-Discrete-RVs-6-1-1">A particular store has an average of 20 customers each hour. During a 4-hour afternoon shift, what is the probability of serving 80 customers.<div class="autopermalink" data-description="Paragraph"><a href="#exercises-Discrete-RVs-6-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+<div class="para" id="exercises-Discrete-RVs-2-3-2-1">
+<span class="process-math">\(\Pr(T = k) = 0.6^{k-1} \cdot 0.4\text{,}\)</span> so every additional flip multiplies the probability by 0.6. Therefore, the highest value for <span class="process-math">\(\Pr(T = k)\)</span> occurs when <span class="process-math">\(k = 1\text{,}\)</span> in which case <span class="process-math">\(\Pr(T = 1) = 0.4.\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-Discrete-RVs-2-3-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
 </div>
-<div class="autopermalink" data-description="Exercise 2.1.5.6"><a href="#exercises-Discrete-RVs-6" title="Copy heading and permalink for Exercise 2.1.5.6" aria-label="Copy heading and permalink for Exercise 2.1.5.6">🔗</a></div></article><article class="exercise exercise-like" id="exercises-Discrete-RVs-7"><h4 class="heading"><span class="codenumber">7<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
+<div class="autopermalink" data-description="Solution 2.1.5.2.b.1"><a href="#exercises-Discrete-RVs-2-3-2" title="Copy heading and permalink for Solution 2.1.5.2.b.1" aria-label="Copy heading and permalink for Solution 2.1.5.2.b.1">🔗</a></div>
-<div class="para" id="exercises-Discrete-RVs-7-1-1">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="#exercises-Discrete-RVs-7-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div></details></div>
+<div class="autopermalink" data-description="Task 2.1.5.2.b"><a href="#exercises-Discrete-RVs-2-3" title="Copy heading and permalink for Task 2.1.5.2.b" aria-label="Copy heading and permalink for Task 2.1.5.2.b">🔗</a></div></article><div class="autopermalink" data-description="Exercise 2.1.5.2"><a href="#exercises-Discrete-RVs-2" title="Copy heading and permalink for Exercise 2.1.5.2" aria-label="Copy heading and permalink for Exercise 2.1.5.2">🔗</a></div></article><article class="exercise exercise-like" id="exercises-Discrete-RVs-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-Discrete-RVs-3-1-1">A particular store has an average of 20 customers each hour. During a 4-hour afternoon shift, what is the probability of serving 80 customers.<div class="autopermalink" data-description="Paragraph"><a href="#exercises-Discrete-RVs-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 2.1.5.7"><a href="#exercises-Discrete-RVs-7" title="Copy heading and permalink for Exercise 2.1.5.7" aria-label="Copy heading and permalink for Exercise 2.1.5.7">🔗</a></div></article><div class="autopermalink" data-description="Exercises 2.1.5"><a href="#exercises-Discrete-RVs" title="Copy heading and permalink for Exercises 2.1.5" aria-label="Copy heading and permalink for Exercises 2.1.5">🔗</a></div></section><div class="autopermalink" data-description="Section 2.1: Discrete Random Variables"><a href="#sec-Discrete-RVs" title="Copy heading and permalink for Section 2.1: Discrete Random Variables" aria-label="Copy heading and permalink for Section 2.1: Discrete Random Variables">🔗</a></div></section></div>
+<div class="solutions"><details id="exercises-Discrete-RVs-3-2" 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="exercises-Discrete-RVs-3-2-1">
+<div class="para">Let <span class="process-math">\(N\)</span> be the number of customers seen during the afternoon shift. Since the store averages 20 customers per hour, it will average 80 per 4-hours. So <span class="process-math">\(N \sim \Poiss(20, 4)\)</span> will have distribution <span class="process-math">\(\Pr(N = k) = \frac{80^{k}}{k!} e^{-80}\text{.}\)</span> Therefore:</div>
+<div class="displaymath process-math" id="exercises-Discrete-RVs-3-2-1-4">
+\begin{gather*}
+\Pr(N = 80) = \frac{80^{80}}{80!} e^{-80} \approx 0.045. 
+\end{gather*}
+</div>
+<div class="autopermalink" data-description="Paragraph"><a href="#exercises-Discrete-RVs-3-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Solution 2.1.5.3.1"><a href="#exercises-Discrete-RVs-3-2" title="Copy heading and permalink for Solution 2.1.5.3.1" aria-label="Copy heading and permalink for Solution 2.1.5.3.1">🔗</a></div>
+</div></details></div>
+<div class="autopermalink" data-description="Exercise 2.1.5.3"><a href="#exercises-Discrete-RVs-3" title="Copy heading and permalink for Exercise 2.1.5.3" aria-label="Copy heading and permalink for Exercise 2.1.5.3">🔗</a></div></article><div class="autopermalink" data-description="Exercises 2.1.5"><a href="#exercises-Discrete-RVs" title="Copy heading and permalink for Exercises 2.1.5" aria-label="Copy heading and permalink for Exercises 2.1.5">🔗</a></div></section><div class="autopermalink" data-description="Section 2.1: Discrete Random Variables"><a href="#sec-Discrete-RVs" title="Copy heading and permalink for Section 2.1: Discrete Random Variables" aria-label="Copy heading and permalink for Section 2.1: Discrete Random Variables">🔗</a></div></section></div>
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@@ -654,30 +654,126 @@ S = H_1 + H_2 + \dotsb + H_n.
 <td class="c m b0 r0 l0 t0 lines">9</td>
 <td class="c m b0 r0 l0 t0 lines">0.1</td>
 </tr>
-</table></div></figure><div class="autopermalink" data-description="Exercise 3.1.4.1"><a href="#exercises-Expected-Value-1" title="Copy heading and permalink for Exercise 3.1.4.1" aria-label="Copy heading and permalink for Exercise 3.1.4.1">🔗</a></div></article><article class="exercise exercise-like" id="exercises-Expected-Value-2"><h4 class="heading"><span class="codenumber">2<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
+</table></div></figure><div class="solutions"><details id="exercises-Expected-Value-1-2" 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="exercises-Expected-Value-1-2-1">4.8.<div class="autopermalink" data-description="Paragraph"><a href="#exercises-Expected-Value-1-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Answer 3.1.4.1.1"><a href="#exercises-Expected-Value-1-2" title="Copy heading and permalink for Answer 3.1.4.1.1" aria-label="Copy heading and permalink for Answer 3.1.4.1.1">🔗</a></div>
+</div></details></div>
+<div class="autopermalink" data-description="Exercise 3.1.4.1"><a href="#exercises-Expected-Value-1" title="Copy heading and permalink for Exercise 3.1.4.1" aria-label="Copy heading and permalink for Exercise 3.1.4.1">🔗</a></div></article><article class="exercise exercise-like" id="exercises-Expected-Value-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="exercises-Expected-Value-2-1-1">Let <span class="process-math">\(X\)</span> and <span class="process-math">\(Y\)</span> be random variables each taking the values 1, 2, 3, 4, 5. Write different distribution tables for <span class="process-math">\(X\)</span> and <span class="process-math">\(Y\)</span> so that they have the same expected value.<div class="autopermalink" data-description="Paragraph"><a href="#exercises-Expected-Value-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="exercises-Expected-Value-2-2" 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">
+<figure class="table table-like" id="exercises-Expected-Value-2-2-1"><figcaption><span class="type">Table</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">3.1.14<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span>Example Distributions<div class="autopermalink" data-description="Table 3.1.14: Example Distributions"><a href="#exercises-Expected-Value-2-2-1" title="Copy heading and permalink for Table 3.1.14: Example Distributions" aria-label="Copy heading and permalink for Table 3.1.14: Example Distributions">🔗</a></div></figcaption><div class="tabular-box natural-width"><table class="tabular">
+<tr>
+<td class="l m b1 r0 l0 t0 lines"><span class="process-math">\(a\)</span></td>
+<td class="l m b1 r0 l0 t0 lines"><span class="process-math">\(\Pr(X = a)\)</span></td>
+<td class="l m b1 r0 l0 t0 lines"><span class="process-math">\(\Pr(Y = a)\)</span></td>
+</tr>
+<tr>
+<td class="l m b0 r0 l0 t0 lines">1</td>
+<td class="l m b0 r0 l0 t0 lines">0.2</td>
+<td class="l m b0 r0 l0 t0 lines">0.1</td>
+</tr>
+<tr>
+<td class="l m b0 r0 l0 t0 lines">2</td>
+<td class="l m b0 r0 l0 t0 lines">0.2</td>
+<td class="l m b0 r0 l0 t0 lines">0.1</td>
+</tr>
+<tr>
+<td class="l m b0 r0 l0 t0 lines">3</td>
+<td class="l m b0 r0 l0 t0 lines">0.2</td>
+<td class="l m b0 r0 l0 t0 lines">0.6</td>
+</tr>
+<tr>
+<td class="l m b0 r0 l0 t0 lines">4</td>
+<td class="l m b0 r0 l0 t0 lines">0.2</td>
+<td class="l m b0 r0 l0 t0 lines">0.1</td>
+</tr>
+<tr>
+<td class="l m b0 r0 l0 t0 lines">5</td>
+<td class="l m b0 r0 l0 t0 lines">0.2</td>
+<td class="l m b0 r0 l0 t0 lines">0.1</td>
+</tr>
+</table></div></figure><div class="autopermalink" data-description="Answer 3.1.4.2.1"><a href="#exercises-Expected-Value-2-2" title="Copy heading and permalink for Answer 3.1.4.2.1" aria-label="Copy heading and permalink for Answer 3.1.4.2.1">🔗</a></div>
+</div></details></div>
 <div class="autopermalink" data-description="Exercise 3.1.4.2"><a href="#exercises-Expected-Value-2" title="Copy heading and permalink for Exercise 3.1.4.2" aria-label="Copy heading and permalink for Exercise 3.1.4.2">🔗</a></div></article><article class="exercise exercise-like" id="exercises-Expected-Value-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-Expected-Value-3-1-1">Suppose we flip a coin <span class="process-math">\(n = 100\)</span> times, and let <span class="process-math">\(N\)</span> count the number of heads. If the coin comes up heads on a flip with probability <span class="process-math">\(p = 0.4\text{,}\)</span> what is <span class="process-math">\(\E(N)\text{?}\)</span> What if <span class="process-math">\(n = 80\)</span> and <span class="process-math">\(p = 0.6\text{?}\)</span> What if <span class="process-math">\(n = 200\)</span> and <span class="process-math">\(p = 0.5\text{?}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-Expected-Value-3-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+<div class="introduction" id="exercises-Expected-Value-3-1"><div class="para" id="exercises-Expected-Value-3-1-1">Suppose we flip a coin <span class="process-math">\(n = 100\)</span> times, and let <span class="process-math">\(N\)</span> count the number of heads.<div class="autopermalink" data-description="Paragraph"><a href="#exercises-Expected-Value-3-1-1" 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-Expected-Value-3-2"><h5 class="heading"><span class="codenumber">(a)</span></h5>
+<div class="para" id="exercises-Expected-Value-3-2-1-1">If the coin comes up heads on a flip with probability <span class="process-math">\(p = 0.4\text{,}\)</span> what is <span class="process-math">\(\E(N)\text{?}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-Expected-Value-3-2-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
 </div>
-<div class="autopermalink" data-description="Exercise 3.1.4.3"><a href="#exercises-Expected-Value-3" title="Copy heading and permalink for Exercise 3.1.4.3" aria-label="Copy heading and permalink for Exercise 3.1.4.3">🔗</a></div></article><article class="exercise exercise-like" id="exercises-Expected-Value-4"><h4 class="heading"><span class="codenumber">4<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
+<div class="solutions"><details id="exercises-Expected-Value-3-2-2" 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="exercises-Expected-Value-3-2-2-1">40.<div class="autopermalink" data-description="Paragraph"><a href="#exercises-Expected-Value-3-2-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Answer 3.1.4.3.a.1"><a href="#exercises-Expected-Value-3-2-2" title="Copy heading and permalink for Answer 3.1.4.3.a.1" aria-label="Copy heading and permalink for Answer 3.1.4.3.a.1">🔗</a></div>
+</div></details></div>
+<div class="autopermalink" data-description="Task 3.1.4.3.a"><a href="#exercises-Expected-Value-3-2" title="Copy heading and permalink for Task 3.1.4.3.a" aria-label="Copy heading and permalink for Task 3.1.4.3.a">🔗</a></div></article><article class="task exercise-like" id="exercises-Expected-Value-3-3"><h5 class="heading"><span class="codenumber">(b)</span></h5>
+<div class="para" id="exercises-Expected-Value-3-3-1-1">What if <span class="process-math">\(n = 80\)</span> and <span class="process-math">\(p = 0.6\text{?}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-Expected-Value-3-3-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="solutions"><details id="exercises-Expected-Value-3-3-2" 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="exercises-Expected-Value-3-3-2-1">48.<div class="autopermalink" data-description="Paragraph"><a href="#exercises-Expected-Value-3-3-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Answer 3.1.4.3.b.1"><a href="#exercises-Expected-Value-3-3-2" title="Copy heading and permalink for Answer 3.1.4.3.b.1" aria-label="Copy heading and permalink for Answer 3.1.4.3.b.1">🔗</a></div>
+</div></details></div>
+<div class="autopermalink" data-description="Task 3.1.4.3.b"><a href="#exercises-Expected-Value-3-3" title="Copy heading and permalink for Task 3.1.4.3.b" aria-label="Copy heading and permalink for Task 3.1.4.3.b">🔗</a></div></article><article class="task exercise-like" id="exercises-Expected-Value-3-4"><h5 class="heading"><span class="codenumber">(c)</span></h5>
+<div class="para" id="exercises-Expected-Value-3-4-1-1">What if <span class="process-math">\(n = 200\)</span> and <span class="process-math">\(p = 0.5\text{?}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-Expected-Value-3-4-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="solutions"><details id="exercises-Expected-Value-3-4-2" 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="exercises-Expected-Value-3-4-2-1">100.<div class="autopermalink" data-description="Paragraph"><a href="#exercises-Expected-Value-3-4-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Answer 3.1.4.3.c.1"><a href="#exercises-Expected-Value-3-4-2" title="Copy heading and permalink for Answer 3.1.4.3.c.1" aria-label="Copy heading and permalink for Answer 3.1.4.3.c.1">🔗</a></div>
+</div></details></div>
+<div class="autopermalink" data-description="Task 3.1.4.3.c"><a href="#exercises-Expected-Value-3-4" title="Copy heading and permalink for Task 3.1.4.3.c" aria-label="Copy heading and permalink for Task 3.1.4.3.c">🔗</a></div></article><div class="autopermalink" data-description="Exercise 3.1.4.3"><a href="#exercises-Expected-Value-3" title="Copy heading and permalink for Exercise 3.1.4.3" aria-label="Copy heading and permalink for Exercise 3.1.4.3">🔗</a></div></article><article class="exercise exercise-like" id="exercises-Expected-Value-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-Expected-Value-4-1-1">If <span class="process-math">\(\E(X) = 3\text{,}\)</span> <span class="process-math">\(\E(Y) = -2\text{,}\)</span> and <span class="process-math">\(\E(Z) = 1\text{,}\)</span> what is <span class="process-math">\(\E(4X + 5Y - Z + 3)\text{?}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-Expected-Value-4-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
 </div>
+<div class="solutions"><details id="exercises-Expected-Value-4-2" 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="exercises-Expected-Value-4-2-1">4.<div class="autopermalink" data-description="Paragraph"><a href="#exercises-Expected-Value-4-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Answer 3.1.4.4.1"><a href="#exercises-Expected-Value-4-2" title="Copy heading and permalink for Answer 3.1.4.4.1" aria-label="Copy heading and permalink for Answer 3.1.4.4.1">🔗</a></div>
+</div></details></div>
 <div class="autopermalink" data-description="Exercise 3.1.4.4"><a href="#exercises-Expected-Value-4" title="Copy heading and permalink for Exercise 3.1.4.4" aria-label="Copy heading and permalink for Exercise 3.1.4.4">🔗</a></div></article><article class="exercise exercise-like" id="exercises-Expected-Value-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="exercises-Expected-Value-5-1-1">A continuous random variable <span class="process-math">\(X\)</span> taking values in <span class="process-math">\([0, 1]\)</span> has p.d.f. <span class="process-math">\(f(x) = 2x\text{.}\)</span> What is <span class="process-math">\(\E(X)\text{?}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-Expected-Value-5-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
 </div>
+<div class="solutions"><details id="exercises-Expected-Value-5-2" 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="exercises-Expected-Value-5-2-1">2/3.<div class="autopermalink" data-description="Paragraph"><a href="#exercises-Expected-Value-5-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Answer 3.1.4.5.1"><a href="#exercises-Expected-Value-5-2" title="Copy heading and permalink for Answer 3.1.4.5.1" aria-label="Copy heading and permalink for Answer 3.1.4.5.1">🔗</a></div>
+</div></details></div>
 <div class="autopermalink" data-description="Exercise 3.1.4.5"><a href="#exercises-Expected-Value-5" title="Copy heading and permalink for Exercise 3.1.4.5" aria-label="Copy heading and permalink for Exercise 3.1.4.5">🔗</a></div></article><article class="exercise exercise-like" id="exercises-Expected-Value-6"><h4 class="heading"><span class="codenumber">6<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
 <div class="para" id="exercises-Expected-Value-6-1-1">A continuous random variable <span class="process-math">\(X\)</span> taking values in <span class="process-math">\([-1, 1]\)</span> has p.d.f. <span class="process-math">\(f(x) = \frac{3x^2}{2}\text{.}\)</span> What is <span class="process-math">\(\E(X)\text{?}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-Expected-Value-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="exercises-Expected-Value-6-2" 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="exercises-Expected-Value-6-2-1">0.<div class="autopermalink" data-description="Paragraph"><a href="#exercises-Expected-Value-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="Answer 3.1.4.6.1"><a href="#exercises-Expected-Value-6-2" title="Copy heading and permalink for Answer 3.1.4.6.1" aria-label="Copy heading and permalink for Answer 3.1.4.6.1">🔗</a></div>
+</div></details></div>
 <div class="autopermalink" data-description="Exercise 3.1.4.6"><a href="#exercises-Expected-Value-6" title="Copy heading and permalink for Exercise 3.1.4.6" aria-label="Copy heading and permalink for Exercise 3.1.4.6">🔗</a></div></article><article class="exercise exercise-like" id="exercises-Expected-Value-7"><h4 class="heading"><span class="codenumber">7<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
 <div class="para" id="exercises-Expected-Value-7-1-1">A continuous random variable <span class="process-math">\(X\)</span> taking values in <span class="process-math">\([1, 4]\)</span> has p.d.f. <span class="process-math">\(f(x) = \frac{4}{3x^2}\text{.}\)</span> What is <span class="process-math">\(\E(X)\text{?}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-Expected-Value-7-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
 </div>
+<div class="solutions"><details id="exercises-Expected-Value-7-2" 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="exercises-Expected-Value-7-2-1">
+<span class="process-math">\(\frac{4}{3}\ln(4) \approx 1.85.\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-Expected-Value-7-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Answer 3.1.4.7.1"><a href="#exercises-Expected-Value-7-2" title="Copy heading and permalink for Answer 3.1.4.7.1" aria-label="Copy heading and permalink for Answer 3.1.4.7.1">🔗</a></div>
+</div></details></div>
 <div class="autopermalink" data-description="Exercise 3.1.4.7"><a href="#exercises-Expected-Value-7" title="Copy heading and permalink for Exercise 3.1.4.7" aria-label="Copy heading and permalink for Exercise 3.1.4.7">🔗</a></div></article><article class="exercise exercise-like" id="exercises-Expected-Value-8"><h4 class="heading"><span class="codenumber">8<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
 <div class="para" id="exercises-Expected-Value-8-1-1">A continuous random variable <span class="process-math">\(X\)</span> taking values in <span class="process-math">\([1, 4]\)</span> has p.d.f. <span class="process-math">\(f(x) = k(x - \sqrt{x})\)</span> for some constant <span class="process-math">\(k\text{.}\)</span> In a previous problem, you found the value of <span class="process-math">\(k\text{.}\)</span> Now, find <span class="process-math">\(\E(X)\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-Expected-Value-8-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
 </div>
+<div class="solutions"><details id="exercises-Expected-Value-8-2" 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="exercises-Expected-Value-8-2-1">
+<span class="process-math">\(E(X) \approx 3.04.\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-Expected-Value-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="Answer 3.1.4.8.1"><a href="#exercises-Expected-Value-8-2" title="Copy heading and permalink for Answer 3.1.4.8.1" aria-label="Copy heading and permalink for Answer 3.1.4.8.1">🔗</a></div>
+</div></details></div>
 <div class="autopermalink" data-description="Exercise 3.1.4.8"><a href="#exercises-Expected-Value-8" title="Copy heading and permalink for Exercise 3.1.4.8" aria-label="Copy heading and permalink for Exercise 3.1.4.8">🔗</a></div></article><article class="exercise exercise-like" id="exercises-Expected-Value-9"><h4 class="heading"><span class="codenumber">9<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
 <div class="para" id="exercises-Expected-Value-9-1-1">A continuous random variable <span class="process-math">\(X\)</span> taking values in <span class="process-math">\([1, 2]\)</span> has p.d.f. <span class="process-math">\(\displaystyle{f(x) = \frac{1}{2}\left(\frac{1}{x^2} + x\right)}\text{.}\)</span> Find <span class="process-math">\(\E(X)\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-Expected-Value-9-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
 </div>
+<div class="solutions"><details id="exercises-Expected-Value-9-2" 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="exercises-Expected-Value-9-2-1">
+<span class="process-math">\(\frac{1}{2}\left( \ln(2) + \frac{7}{3}\right) \approx 1.513.\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-Expected-Value-9-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Answer 3.1.4.9.1"><a href="#exercises-Expected-Value-9-2" title="Copy heading and permalink for Answer 3.1.4.9.1" aria-label="Copy heading and permalink for Answer 3.1.4.9.1">🔗</a></div>
+</div></details></div>
 <div class="autopermalink" data-description="Exercise 3.1.4.9"><a href="#exercises-Expected-Value-9" title="Copy heading and permalink for Exercise 3.1.4.9" aria-label="Copy heading and permalink for Exercise 3.1.4.9">🔗</a></div></article><div class="autopermalink" data-description="Exercises 3.1.4"><a href="#exercises-Expected-Value" title="Copy heading and permalink for Exercises 3.1.4" aria-label="Copy heading and permalink for Exercises 3.1.4">🔗</a></div></section><div class="autopermalink" data-description="Section 3.1: Expected Value"><a href="#sec-Expected-Value" title="Copy heading and permalink for Section 3.1: Expected Value" aria-label="Copy heading and permalink for Section 3.1: Expected Value">🔗</a></div></section></div>
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sec-Independent-Events.html

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sec-Introduction.html

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sec-Joint-Distributions.html

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+<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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@@ -366,9 +366,64 @@ eBookConfig.enable_chatcodes =  false;
 <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="exercises-Joint-Distributions-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-Joint-Distributions-1-1-1">TODO<div class="autopermalink" data-description="Paragraph"><a href="#exercises-Joint-Distributions-1-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+<div class="para" id="exercises-Joint-Distributions-1-1-1">Consider <span class="process-math">\(X, Y\)</span> with the joint distribution table below. Are <span class="process-math">\(X, Y\)</span> independent?<div class="autopermalink" data-description="Paragraph"><a href="#exercises-Joint-Distributions-1-1-1" 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-Joint-Distributions-1-1-2"><figcaption><span class="type">Table</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">2.3.6<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span>Joint distribution for <span class="process-math">\(X, Y\)</span><div class="autopermalink" data-description="Table 2.3.6: Joint distribution for X, Y"><a href="#exercises-Joint-Distributions-1-1-2" title="Copy heading and permalink for Table 2.3.6: Joint distribution for X, Y" aria-label="Copy heading and permalink for Table 2.3.6: Joint distribution for X, Y">🔗</a></div></figcaption><div class="tabular-box natural-width"><table class="tabular">
+<tr>
+<td class="c m b1 r1 l0 t0 lines"></td>
+<td class="c m b1 r1 l0 t0 lines"><span class="process-math">\(X = 0\)</span></td>
+<td class="c m b1 r0 l0 t0 lines"><span class="process-math">\(X = 1\)</span></td>
+</tr>
+<tr>
+<td class="c m b1 r1 l0 t0 lines"><span class="process-math">\(Y = 0\)</span></td>
+<td class="c m b1 r1 l0 t0 lines">0.2</td>
+<td class="c m b1 r0 l0 t0 lines">0.3</td>
+</tr>
+<tr>
+<td class="c m b0 r1 l0 t0 lines"><span class="process-math">\(Y = 1\)</span></td>
+<td class="c m b0 r1 l0 t0 lines">0.4</td>
+<td class="c m b0 r0 l0 t0 lines">0.1</td>
+</tr>
+</table></div></figure><div class="solutions"><details id="exercises-Joint-Distributions-1-2" 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="exercises-Joint-Distributions-1-2-1">No. For example, <span class="process-math">\(\Pr(X = 0, Y = 0) \neq \Pr(X = 0)\Pr(Y = 0).\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-Joint-Distributions-1-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
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-<div class="autopermalink" data-description="Exercise 2.3.1"><a href="#exercises-Joint-Distributions-1" title="Copy heading and permalink for Exercise 2.3.1" aria-label="Copy heading and permalink for Exercise 2.3.1">🔗</a></div></article><div class="autopermalink" data-description="Exercises 2.3"><a href="#exercises-Joint-Distributions" title="Copy heading and permalink for Exercises 2.3" aria-label="Copy heading and permalink for Exercises 2.3">🔗</a></div></section><div class="autopermalink" data-description="Section 2.3: Joint Distributions"><a href="#sec-Joint-Distributions" title="Copy heading and permalink for Section 2.3: Joint Distributions" aria-label="Copy heading and permalink for Section 2.3: Joint Distributions">🔗</a></div></section></div>
+<div class="autopermalink" data-description="Answer 2.3.1.1"><a href="#exercises-Joint-Distributions-1-2" title="Copy heading and permalink for Answer 2.3.1.1" aria-label="Copy heading and permalink for Answer 2.3.1.1">🔗</a></div>
+</div></details></div>
+<div class="autopermalink" data-description="Exercise 2.3.1"><a href="#exercises-Joint-Distributions-1" title="Copy heading and permalink for Exercise 2.3.1" aria-label="Copy heading and permalink for Exercise 2.3.1">🔗</a></div></article><article class="exercise exercise-like" id="exercises-Joint-Distributions-2"><h4 class="heading"><span class="codenumber">2<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
+<div class="para logical" id="exercises-Joint-Distributions-2-1-1">
+<div class="para">Suppose <span class="process-math">\(X, Y\)</span> have the distributions:</div>
+<div class="displaymath process-math" id="exercises-Joint-Distributions-2-1-1-2">
+\begin{align*}
+\Pr(X = 0) \amp = 0.1 \amp \Pr(Y = 0) \amp = 0.4 \\
+\Pr(X = 1) \amp = 0.4 \amp \Pr(Y = 1) \amp = 0.6 \\
+\Pr(X = 2) \amp = 0.5  
+\end{align*}
+</div>
+<div class="para">Assuming <span class="process-math">\(X, Y\)</span> are independent, write a joint distribution table.</div>
+<div class="autopermalink" data-description="Paragraph"><a href="#exercises-Joint-Distributions-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="exercises-Joint-Distributions-2-2" 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">
+<figure class="table table-like" id="exercises-Joint-Distributions-2-2-1"><figcaption><span class="type">Table</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">2.3.7<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span>Joint Distribution<div class="autopermalink" data-description="Table 2.3.7: Joint Distribution"><a href="#exercises-Joint-Distributions-2-2-1" title="Copy heading and permalink for Table 2.3.7: Joint Distribution" aria-label="Copy heading and permalink for Table 2.3.7: Joint Distribution">🔗</a></div></figcaption><div class="tabular-box natural-width"><table class="tabular">
+<tr>
+<td class="c m b1 r1 l0 t0 lines"></td>
+<td class="c m b1 r1 l0 t0 lines"><span class="process-math">\(X = 0\)</span></td>
+<td class="c m b1 r1 l0 t0 lines"><span class="process-math">\(X = 1\)</span></td>
+<td class="c m b1 r0 l0 t0 lines"><span class="process-math">\(X = 2\)</span></td>
+</tr>
+<tr>
+<td class="c m b1 r1 l0 t0 lines"><span class="process-math">\(Y = 0\)</span></td>
+<td class="c m b1 r1 l0 t0 lines">0.04</td>
+<td class="c m b1 r1 l0 t0 lines">0.16</td>
+<td class="c m b1 r0 l0 t0 lines">0.2</td>
+</tr>
+<tr>
+<td class="c m b0 r1 l0 t0 lines"><span class="process-math">\(Y = 1\)</span></td>
+<td class="c m b0 r1 l0 t0 lines">0.06</td>
+<td class="c m b0 r1 l0 t0 lines">0.24</td>
+<td class="c m b0 r0 l0 t0 lines">0.3</td>
+</tr>
+</table></div></figure><div class="autopermalink" data-description="Answer 2.3.2.1"><a href="#exercises-Joint-Distributions-2-2" title="Copy heading and permalink for Answer 2.3.2.1" aria-label="Copy heading and permalink for Answer 2.3.2.1">🔗</a></div>
+</div></details></div>
+<div class="autopermalink" data-description="Exercise 2.3.2"><a href="#exercises-Joint-Distributions-2" title="Copy heading and permalink for Exercise 2.3.2" aria-label="Copy heading and permalink for Exercise 2.3.2">🔗</a></div></article><div class="autopermalink" data-description="Exercises 2.3"><a href="#exercises-Joint-Distributions" title="Copy heading and permalink for Exercises 2.3" aria-label="Copy heading and permalink for Exercises 2.3">🔗</a></div></section><div class="autopermalink" data-description="Section 2.3: Joint Distributions"><a href="#sec-Joint-Distributions" title="Copy heading and permalink for Section 2.3: Joint Distributions" aria-label="Copy heading and permalink for Section 2.3: Joint Distributions">🔗</a></div></section></div>
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sec-Linear-Regression.html

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sec-One-Sample-Tests.html

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+<link rel="stylesheet" type="text/css" href="_static/prefix-runestone.6ec5960970d8b364.css">
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sec-Power.html

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sec-Probability.html

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+eBookConfig.runestone_version = '7.11.11';
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+<link rel="stylesheet" type="text/css" href="_static/prefix-runestone.6ec5960970d8b364.css">
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sec-Set-Theory.html

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sec-Two-Sample-Tests.html

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 eBookConfig.enable_chatcodes =  false;
 </script>
 <!--*** Runestone Services ***-->
-<script src="_static/prefix-runtime.991c135ccf182bf5.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.1c010553c35c544c.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
+<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">
-<link rel="stylesheet" type="text/css" href="_static/prefix-runestone.677a75a9120449ff.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>
 </head>

sec-Variance.html

@@ -101,15 +101,15 @@ eBookConfig.allow_pairs = false;
 eBookConfig.enableScratchAC = false;
 eBookConfig.build_info = "";
 eBookConfig.python3 = null;
-eBookConfig.runestone_version = '7.11.8';
+eBookConfig.runestone_version = '7.11.11';
 eBookConfig.jobehost = '';
 eBookConfig.proxyuri_runs = '';
 eBookConfig.proxyuri_files = '';
 eBookConfig.enable_chatcodes =  false;
 </script>
 <!--*** Runestone Services ***-->
-<script src="_static/prefix-runtime.991c135ccf182bf5.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.1c010553c35c544c.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
+<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">
-<link rel="stylesheet" type="text/css" href="_static/prefix-runestone.677a75a9120449ff.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>
 </head>