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2026-02-26 10:10:34 -05:00
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commit d39892d81d
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@@ -62,7 +62,7 @@ window.MathJax = {
"[pretext]/mathjaxknowl3.js"
],
"paths": {
"pretext": "_static/pretext/js/lib"
"pretext": "_static/pretext/js"
}
},
"startup": {
@@ -79,7 +79,7 @@ window.MathJax = {
<meta property="og:type" content="book">
<meta property="book:title" content="Introduction to Probability and Statistics for the Life Sciences">
<meta property="book:author" content="Andy Eisenberg">
<script src="_static/pretext/js/lib/jquery.min.js"></script><script src="_static/pretext/js/lib/jquery.sticky.js"></script><script src="_static/pretext/js/lib/jquery.espy.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><script src="_static/pretext/js/user_preferences.js"></script><!--** eBookCongig is necessary to configure interactive **-->
<script src="_static/pretext/js/jquery.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><!--** eBookCongig is necessary to configure interactive **-->
<!--** Runestone components to run locally in reader's browser **-->
<!--** No external communication: **-->
<!--** log level is 0, Runestone Services are disabled **-->
@@ -101,16 +101,16 @@ eBookConfig.allow_pairs = false;
eBookConfig.enableScratchAC = false;
eBookConfig.build_info = "";
eBookConfig.python3 = null;
eBookConfig.runestone_version = '7.11.14';
eBookConfig.runestone_version = '7.11.15';
eBookConfig.jobehost = '';
eBookConfig.proxyuri_runs = '';
eBookConfig.proxyuri_files = '';
eBookConfig.enable_chatcodes = false;
</script>
<!--*** Runestone Services ***-->
<script src="_static/prefix-runtime.d892923478694492.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.1d6e4aba17c2c7f2.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
<script src="_static/prefix-runtime.529fd9398bfbd03e.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.1d6e4aba17c2c7f2.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
<link rel="stylesheet" type="text/css" href="_static/prefix-runestone.6ec5960970d8b364.css">
<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/lib/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
</script>
</head>
<body class="pretext book ignore-math">
@@ -146,6 +146,7 @@ eBookConfig.enable_chatcodes = false;
\DeclareMathOperator{\Geom}{Geom}
\DeclareMathOperator{\Poiss}{Poiss}
\DeclareMathOperator{\Exp}{Exp}
\DeclareMathOperator{\Norm}{N}
\DeclareMathOperator{\E}{E}
@@ -231,6 +232,17 @@ eBookConfig.enable_chatcodes = false;
<div class="toc-title-box"><a href="notes-02-10.html" class="internal"><span class="title">Tuesday, Feb 10</span></a></div>
<ul class="structural toc-item-list"><li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-02-10.html#notes-02-10-3" class="internal"><span class="title">Likelihood</span></a></div></li></ul>
</li>
<li class="toc-item toc-section">
<div class="toc-title-box"><a href="notes-02-19.html" class="internal"><span class="title">Thursday, Feb 19</span></a></div>
<ul class="structural toc-item-list"><li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-02-19.html#notes-02-19-3" class="internal"><span class="title">Central Limit Theorem</span></a></div></li></ul>
</li>
<li class="toc-item toc-section">
<div class="toc-title-box"><a href="notes-02-24.html" class="internal"><span class="title">Tuesday, Feb 24</span></a></div>
<ul class="structural toc-item-list">
<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-02-24.html#notes-02-24-3" class="internal"><span class="title">More Central Limit Theorem</span></a></div></li>
<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-02-24.html#notes-02-24-4" class="internal"><span class="title">Confidence Intervals</span></a></div></li>
</ul>
</li>
</ul>
</li>
<li class="toc-item toc-chapter">
@@ -329,16 +341,28 @@ eBookConfig.enable_chatcodes = false;
</div>
<div class="sbsgroup">
<div class="sidebyside"><div class="sbsrow" style="margin-left:5%;margin-right:5%;grid-template-columns:44.4444444444444% 44.4444444444444%;column-gap:10%;">
<div class="sbspanel sbspanel--top top" style=""><figure class="figure figure-like" id="fig-Venn-diagram-union"><img src="generated/latex-image/fig-Venn-diagram-union-2.svg" role="img" class="contained" alt="described in detail following the image" aria-describedby="fig-Venn-diagram-union-2-description"><details class="image-description" aria-live="polite"><summary title="details"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe88e;</span></summary><div id="fig-Venn-diagram-union-2-description"><div class="para" id="fig-Venn-diagram-union-2-1-1">Venn diagram showing sets <span class="process-math">\(A, B\)</span> with the region representing <span class="process-math">\(A \cup B\)</span> shaded.<div class="autopermalink" data-description="Paragraph"><a href="#fig-Venn-diagram-union-2-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
</div></div></details><figcaption><span class="type">Figure</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">7<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span>Union<div class="autopermalink" data-description="Figure 7"><a href="#fig-Venn-diagram-union" title="Copy heading and permalink for Figure 7" aria-label="Copy heading and permalink for Figure 7">🔗</a></div></figcaption></figure></div>
<div class="sbspanel sbspanel--top top" style=""><figure class="figure figure-like" id="fig-Venn-diagram-intersection"><img src="generated/latex-image/fig-Venn-diagram-intersection-2.svg" role="img" class="contained" alt="described in detail following the image" aria-describedby="fig-Venn-diagram-intersection-2-description"><details class="image-description" aria-live="polite"><summary title="details"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe88e;</span></summary><div id="fig-Venn-diagram-intersection-2-description"><div class="para" id="fig-Venn-diagram-intersection-2-1-1">Venn diagram showing sets <span class="process-math">\(A, B\)</span> with the region representing <span class="process-math">\(A \cap B\)</span> shaded.<div class="autopermalink" data-description="Paragraph"><a href="#fig-Venn-diagram-intersection-2-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
</div></div></details><figcaption><span class="type">Figure</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">8<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span>Intersection<div class="autopermalink" data-description="Figure 8"><a href="#fig-Venn-diagram-intersection" title="Copy heading and permalink for Figure 8" aria-label="Copy heading and permalink for Figure 8">🔗</a></div></figcaption></figure></div>
<div class="sbspanel sbspanel--top top" style=""><figure class="figure figure-like" id="fig-Venn-diagram-union"><div class="image-box">
<img src="generated/latex-image/fig-Venn-diagram-union-2.svg" role="img" class="contained" alt="described in detail following the image" aria-describedby="fig-Venn-diagram-union-2-description"><details class="image-description" aria-live="polite"><summary title="details"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe88e;</span></summary><div id="fig-Venn-diagram-union-2-description"><div class="para" id="fig-Venn-diagram-union-2-1-1">Venn diagram showing sets <span class="process-math">\(A, B\)</span> with the region representing <span class="process-math">\(A \cup B\)</span> shaded.<div class="autopermalink" data-description="Paragraph"><a href="#fig-Venn-diagram-union-2-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
</div></div></details>
</div>
<figcaption><span class="type">Figure</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">7<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span>Union<div class="autopermalink" data-description="Figure 7"><a href="#fig-Venn-diagram-union" title="Copy heading and permalink for Figure 7" aria-label="Copy heading and permalink for Figure 7">🔗</a></div></figcaption></figure></div>
<div class="sbspanel sbspanel--top top" style=""><figure class="figure figure-like" id="fig-Venn-diagram-intersection"><div class="image-box">
<img src="generated/latex-image/fig-Venn-diagram-intersection-2.svg" role="img" class="contained" alt="described in detail following the image" aria-describedby="fig-Venn-diagram-intersection-2-description"><details class="image-description" aria-live="polite"><summary title="details"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe88e;</span></summary><div id="fig-Venn-diagram-intersection-2-description"><div class="para" id="fig-Venn-diagram-intersection-2-1-1">Venn diagram showing sets <span class="process-math">\(A, B\)</span> with the region representing <span class="process-math">\(A \cap B\)</span> shaded.<div class="autopermalink" data-description="Paragraph"><a href="#fig-Venn-diagram-intersection-2-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
</div></div></details>
</div>
<figcaption><span class="type">Figure</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">8<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span>Intersection<div class="autopermalink" data-description="Figure 8"><a href="#fig-Venn-diagram-intersection" title="Copy heading and permalink for Figure 8" aria-label="Copy heading and permalink for Figure 8">🔗</a></div></figcaption></figure></div>
</div></div>
<div class="sidebyside"><div class="sbsrow" style="margin-left:5%;margin-right:5%;grid-template-columns:44.4444444444444% 44.4444444444444%;column-gap:10%;">
<div class="sbspanel sbspanel--top top" style=""><figure class="figure figure-like" id="fig-Venn-diagram-difference"><img src="generated/latex-image/fig-Venn-diagram-difference-2.svg" role="img" class="contained" alt="described in detail following the image" aria-describedby="fig-Venn-diagram-difference-2-description"><details class="image-description" aria-live="polite"><summary title="details"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe88e;</span></summary><div id="fig-Venn-diagram-difference-2-description"><div class="para" id="fig-Venn-diagram-difference-2-1-1">Venn diagram showing sets <span class="process-math">\(A, B\)</span> with the region representing <span class="process-math">\(A - B\)</span> shaded.<div class="autopermalink" data-description="Paragraph"><a href="#fig-Venn-diagram-difference-2-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
</div></div></details><figcaption><span class="type">Figure</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">9<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span>Difference<div class="autopermalink" data-description="Figure 9"><a href="#fig-Venn-diagram-difference" title="Copy heading and permalink for Figure 9" aria-label="Copy heading and permalink for Figure 9">🔗</a></div></figcaption></figure></div>
<div class="sbspanel sbspanel--top top" style=""><figure class="figure figure-like" id="fig-Venn-diagram-complement"><img src="generated/latex-image/fig-Venn-diagram-complement-2.svg" role="img" class="contained" alt="described in detail following the image" aria-describedby="fig-Venn-diagram-complement-2-description"><details class="image-description" aria-live="polite"><summary title="details"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe88e;</span></summary><div id="fig-Venn-diagram-complement-2-description"><div class="para" id="fig-Venn-diagram-complement-2-1-1">Venn diagram showing set <span class="process-math">\(A \subset \Omega\)</span> with the region representing <span class="process-math">\(A^c\)</span> shaded.<div class="autopermalink" data-description="Paragraph"><a href="#fig-Venn-diagram-complement-2-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
</div></div></details><figcaption><span class="type">Figure</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">10<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span>Complement<div class="autopermalink" data-description="Figure 10"><a href="#fig-Venn-diagram-complement" title="Copy heading and permalink for Figure 10" aria-label="Copy heading and permalink for Figure 10">🔗</a></div></figcaption></figure></div>
<div class="sbspanel sbspanel--top top" style=""><figure class="figure figure-like" id="fig-Venn-diagram-difference"><div class="image-box">
<img src="generated/latex-image/fig-Venn-diagram-difference-2.svg" role="img" class="contained" alt="described in detail following the image" aria-describedby="fig-Venn-diagram-difference-2-description"><details class="image-description" aria-live="polite"><summary title="details"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe88e;</span></summary><div id="fig-Venn-diagram-difference-2-description"><div class="para" id="fig-Venn-diagram-difference-2-1-1">Venn diagram showing sets <span class="process-math">\(A, B\)</span> with the region representing <span class="process-math">\(A - B\)</span> shaded.<div class="autopermalink" data-description="Paragraph"><a href="#fig-Venn-diagram-difference-2-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
</div></div></details>
</div>
<figcaption><span class="type">Figure</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">9<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span>Difference<div class="autopermalink" data-description="Figure 9"><a href="#fig-Venn-diagram-difference" title="Copy heading and permalink for Figure 9" aria-label="Copy heading and permalink for Figure 9">🔗</a></div></figcaption></figure></div>
<div class="sbspanel sbspanel--top top" style=""><figure class="figure figure-like" id="fig-Venn-diagram-complement"><div class="image-box">
<img src="generated/latex-image/fig-Venn-diagram-complement-2.svg" role="img" class="contained" alt="described in detail following the image" aria-describedby="fig-Venn-diagram-complement-2-description"><details class="image-description" aria-live="polite"><summary title="details"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe88e;</span></summary><div id="fig-Venn-diagram-complement-2-description"><div class="para" id="fig-Venn-diagram-complement-2-1-1">Venn diagram showing set <span class="process-math">\(A \subset \Omega\)</span> with the region representing <span class="process-math">\(A^c\)</span> shaded.<div class="autopermalink" data-description="Paragraph"><a href="#fig-Venn-diagram-complement-2-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
</div></div></details>
</div>
<figcaption><span class="type">Figure</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">10<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span>Complement<div class="autopermalink" data-description="Figure 10"><a href="#fig-Venn-diagram-complement" title="Copy heading and permalink for Figure 10" aria-label="Copy heading and permalink for Figure 10">🔗</a></div></figcaption></figure></div>
</div></div>
</div>
<div class="autopermalink" data-description="Subsection: Sec 1.1: Sets"><a href="#subsec-Sets" title="Copy heading and permalink for Subsection: Sec 1.1: Sets" aria-label="Copy heading and permalink for Subsection: Sec 1.1: Sets">🔗</a></div></section><section class="subsection" id="subsec-Probability"><h3 class="heading hide-type">