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<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Power.html#exercises-Power" class="internal"><span class="codenumber">5.3</span> <span class="title">Exercises</span></a></div></li></ul>
|
||||
</li>
|
||||
<li class="toc-item toc-section">
|
||||
<div class="toc-title-box"><a href="sec-Chi-Squared.html" class="internal"><span class="codenumber">5.4</span> <span class="title"><span class="process-math">\(\chi^2\)</span> Test</span></a></div>
|
||||
<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Chi-Squared.html#exercises-Chi-Squared" class="internal"><span class="codenumber">5.4</span> <span class="title">Exercises</span></a></div></li></ul>
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toc-item toc-chapter">
|
||||
<div class="toc-title-box"><a href="ch-Linear-Regression.html" class="internal"><span class="codenumber">6</span> <span class="title">Linear Regression</span></a></div>
|
||||
<ul class="structural toc-item-list">
|
||||
<li class="toc-item toc-section">
|
||||
<div class="toc-title-box"><a href="sec-Correlation.html" class="internal"><span class="codenumber">6.1</span> <span class="title">Correlation</span></a></div>
|
||||
<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Correlation.html#exercises-Correlation" class="internal"><span class="codenumber">6.1</span> <span class="title">Exercises</span></a></div></li></ul>
|
||||
</li>
|
||||
<li class="toc-item toc-section">
|
||||
<div class="toc-title-box"><a href="sec-Linear-Regression.html" class="internal"><span class="codenumber">6.2</span> <span class="title">Linear Regression</span></a></div>
|
||||
<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Linear-Regression.html#exercises-Linear-Regression" class="internal"><span class="codenumber">6.2</span> <span class="title">Exercises</span></a></div></li></ul>
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toc-item toc-backmatter contains-active">
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<div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div>
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<ul class="structural toc-item-list contains-active">
|
||||
<li class="toc-item toc-appendix">
|
||||
<div class="toc-title-box"><a href="backmatter-2.html" class="internal"><span class="codenumber">A</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table</span></a></div>
|
||||
<ul class="structural toc-item-list"><li class="toc-item toc-section"><div class="toc-title-box"><a href="app-Phi-table.html" class="internal"><span class="codenumber">A.1</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table of Values</span></a></div></li></ul>
|
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<li class="toc-item toc-colophon active"><div class="toc-title-box"><a href="backmatter-3.html" class="internal"><span class="title">Colophon</span></a></div></li>
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<div class="para" id="backmatter-3-1">This book was authored in PreTeXt.<div class="autopermalink" data-description="Paragraph"><a href="#backmatter-3-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
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<a class="pretext-link" href="https://pretextbook.org" title="PreTeXt"><div class="logo"><svg xmlns="http://www.w3.org/2000/svg" height="100%" viewBox="338 3000 8772 6866" role="img"><title>PreTeXt logo</title><g style="stroke-width:.025in; stroke:currentColor; fill:none"><polyline points="472,3590 472,9732 " style="stroke-width:174; stroke-linejoin:miter; stroke-linecap:round; "></polyline><path style="stroke-width:126;stroke-linecap:butt;" d="M 4724,9448 A 4660 4660 0 0 1 8598 9259"></path><path style="stroke-width:174;stroke-linecap:butt;" d="M 4488,9685 A 4228 4228 0 0 0 472 9732"></path><path style="stroke-width:126;stroke-linecap:butt;" d="M 4724,3590 A 4241 4241 0 0 1 8598 3496"></path><path style="stroke-width:126;stroke-linecap:round;" d="M 850,3496 A 4241 4241 0 0 1 4724 3590"></path><path style="stroke-width:126;stroke-linecap:round;" d="M 850,9259 A 4507 4507 0 0 1 4724 9448"></path><polyline points="5385,4299 4062,8125" style="stroke-width:300; stroke-linejoin:miter; stroke-linecap:round;"></polyline><polyline points="8598,3496 8598,9259" style="stroke-width:126; stroke-linejoin:miter; stroke-linecap:round;"></polyline><polyline points="850,3496 850,9259" style="stroke-width:126; stroke-linejoin:miter; stroke-linecap:round;"></polyline><polyline points="4960,9685 4488,9685" style="stroke-width:174; stroke-linejoin:miter; stroke-linecap:round;"></polyline><polyline points="3070,4582 1889,6141 3070,7700" style="stroke-width:300; stroke-linejoin:miter; stroke-linecap:round;"></polyline><polyline points="6418,4582 7600,6141 6418,7700" style="stroke-width:300; stroke-linejoin:miter; stroke-linecap:round;"></polyline><polyline points="8976,3590 8976,9732" style="stroke-width:174; stroke-linejoin:miter; stroke-linecap:round;"></polyline><path style="stroke-width:174;stroke-linecap:butt;" d="M 4960,9685 A 4228 4228 0 0 1 8976 9732"></path></g></svg></div></a><a class="runestone-link" href="https://runestone.academy" title="Runestone Academy"><img class="logo" src="https://runestone.academy/runestone/static/images/RAIcon_cropped.png" alt="Runstone Academy logo"></a><a class="mathjax-link" href="https://www.mathjax.org" title="MathJax"><img class="logo" src="https://www.mathjax.org/badge/badge-square-2.png" alt="MathJax logo"></a>
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</body>
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</html>
|
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+17
-4
@@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false;
|
||||
eBookConfig.enableScratchAC = false;
|
||||
eBookConfig.build_info = "";
|
||||
eBookConfig.python3 = null;
|
||||
eBookConfig.runestone_version = '7.11.13';
|
||||
eBookConfig.runestone_version = '7.11.14';
|
||||
eBookConfig.jobehost = '';
|
||||
eBookConfig.proxyuri_runs = '';
|
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eBookConfig.proxyuri_files = '';
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</script>
|
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<!--*** Runestone Services ***-->
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<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
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<script src="_static/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">
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<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
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</script>
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||||
@@ -146,6 +146,7 @@ eBookConfig.enable_chatcodes = false;
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\DeclareMathOperator{\Geom}{Geom}
|
||||
\DeclareMathOperator{\Poiss}{Poiss}
|
||||
\DeclareMathOperator{\Exp}{Exp}
|
||||
\DeclareMathOperator{\Norm}{N}
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||||
|
||||
|
||||
\DeclareMathOperator{\E}{E}
|
||||
@@ -294,9 +295,21 @@ eBookConfig.enable_chatcodes = false;
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toc-item toc-backmatter active"><div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div></li>
|
||||
<li class="toc-item toc-backmatter contains-active">
|
||||
<div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div>
|
||||
<ul class="structural toc-item-list active">
|
||||
<li class="toc-item toc-appendix">
|
||||
<div class="toc-title-box"><a href="backmatter-2.html" class="internal"><span class="codenumber">A</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table</span></a></div>
|
||||
<ul class="structural toc-item-list"><li class="toc-item toc-section"><div class="toc-title-box"><a href="app-Phi-table.html" class="internal"><span class="codenumber">A.1</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table of Values</span></a></div></li></ul>
|
||||
</li>
|
||||
<li class="toc-item toc-colophon"><div class="toc-title-box"><a href="backmatter-3.html" class="internal"><span class="title">Colophon</span></a></div></li>
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||||
</ul>
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</ul></nav></div>
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<main class="ptx-main"><div id="ptx-content" class="ptx-content"><section class="backmatter" id="backmatter"><nav class="summary-links"><ul><li><a href="backmatter-2.html" class="internal"><span class="title">Colophon</span></a></li></ul></nav><div class="autopermalink" data-description="Back Matter: Backmatter"><a href="#backmatter" title="Copy heading and permalink for Back Matter: Backmatter" aria-label="Copy heading and permalink for Back Matter: Backmatter">🔗</a></div></section></div>
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||||
<main class="ptx-main"><div id="ptx-content" class="ptx-content"><section class="backmatter" id="backmatter"><nav class="summary-links"><ul>
|
||||
<li><a href="backmatter-2.html" class="internal"><span class="codenumber">A</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table</span></a></li>
|
||||
<li><a href="backmatter-3.html" class="internal"><span class="title">Colophon</span></a></li>
|
||||
</ul></nav><div class="autopermalink" data-description="Back Matter: Backmatter"><a href="#backmatter" title="Copy heading and permalink for Back Matter: Backmatter" aria-label="Copy heading and permalink for Back Matter: Backmatter">🔗</a></div></section></div>
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<div id="ptx-content-footer" class="ptx-content-footer">
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<a class="previous-button button" href="sec-Linear-Regression.html" title="Previous"><span class="icon material-symbols-outlined" aria-hidden="true"></span><span class="name">Prev</span></a><a class="top-button button" href="#" title="Top"><span class="icon material-symbols-outlined" aria-hidden="true"></span><span class="name">Top</span></a><a class="next-button button" href="backmatter-2.html" title="Next"><span class="name">Next</span><span class="icon material-symbols-outlined" aria-hidden="true"></span></a>
|
||||
</div></main>
|
||||
|
||||
@@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false;
|
||||
eBookConfig.enableScratchAC = false;
|
||||
eBookConfig.build_info = "";
|
||||
eBookConfig.python3 = null;
|
||||
eBookConfig.runestone_version = '7.11.13';
|
||||
eBookConfig.runestone_version = '7.11.14';
|
||||
eBookConfig.jobehost = '';
|
||||
eBookConfig.proxyuri_runs = '';
|
||||
eBookConfig.proxyuri_files = '';
|
||||
eBookConfig.enable_chatcodes = false;
|
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</script>
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<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
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<script src="_static/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">
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<link rel="stylesheet" type="text/css" href="_static/prefix-runestone.6ec5960970d8b364.css">
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<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
|
||||
</script>
|
||||
@@ -146,6 +146,7 @@ eBookConfig.enable_chatcodes = false;
|
||||
\DeclareMathOperator{\Geom}{Geom}
|
||||
\DeclareMathOperator{\Poiss}{Poiss}
|
||||
\DeclareMathOperator{\Exp}{Exp}
|
||||
\DeclareMathOperator{\Norm}{N}
|
||||
|
||||
|
||||
\DeclareMathOperator{\E}{E}
|
||||
@@ -294,7 +295,16 @@ eBookConfig.enable_chatcodes = false;
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toc-item toc-backmatter"><div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div></li>
|
||||
<li class="toc-item toc-backmatter">
|
||||
<div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div>
|
||||
<ul class="structural toc-item-list">
|
||||
<li class="toc-item toc-appendix">
|
||||
<div class="toc-title-box"><a href="backmatter-2.html" class="internal"><span class="codenumber">A</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table</span></a></div>
|
||||
<ul class="structural toc-item-list"><li class="toc-item toc-section"><div class="toc-title-box"><a href="app-Phi-table.html" class="internal"><span class="codenumber">A.1</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table of Values</span></a></div></li></ul>
|
||||
</li>
|
||||
<li class="toc-item toc-colophon"><div class="toc-title-box"><a href="backmatter-3.html" class="internal"><span class="title">Colophon</span></a></div></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul></nav></div>
|
||||
<main class="ptx-main"><div id="ptx-content" class="ptx-content"><section class="chapter" id="ch-Confidence-Intervals"><h2 class="heading">
|
||||
<span class="type">Chapter</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Confidence Intervals</span>
|
||||
|
||||
+13
-3
@@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false;
|
||||
eBookConfig.enableScratchAC = false;
|
||||
eBookConfig.build_info = "";
|
||||
eBookConfig.python3 = null;
|
||||
eBookConfig.runestone_version = '7.11.13';
|
||||
eBookConfig.runestone_version = '7.11.14';
|
||||
eBookConfig.jobehost = '';
|
||||
eBookConfig.proxyuri_runs = '';
|
||||
eBookConfig.proxyuri_files = '';
|
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eBookConfig.enable_chatcodes = false;
|
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</script>
|
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<!--*** Runestone Services ***-->
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<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
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||||
<script src="_static/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">
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<link rel="stylesheet" type="text/css" href="_static/prefix-runestone.6ec5960970d8b364.css">
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<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
|
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</script>
|
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@@ -146,6 +146,7 @@ eBookConfig.enable_chatcodes = false;
|
||||
\DeclareMathOperator{\Geom}{Geom}
|
||||
\DeclareMathOperator{\Poiss}{Poiss}
|
||||
\DeclareMathOperator{\Exp}{Exp}
|
||||
\DeclareMathOperator{\Norm}{N}
|
||||
|
||||
|
||||
\DeclareMathOperator{\E}{E}
|
||||
@@ -294,7 +295,16 @@ eBookConfig.enable_chatcodes = false;
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toc-item toc-backmatter"><div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div></li>
|
||||
<li class="toc-item toc-backmatter">
|
||||
<div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div>
|
||||
<ul class="structural toc-item-list">
|
||||
<li class="toc-item toc-appendix">
|
||||
<div class="toc-title-box"><a href="backmatter-2.html" class="internal"><span class="codenumber">A</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table</span></a></div>
|
||||
<ul class="structural toc-item-list"><li class="toc-item toc-section"><div class="toc-title-box"><a href="app-Phi-table.html" class="internal"><span class="codenumber">A.1</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table of Values</span></a></div></li></ul>
|
||||
</li>
|
||||
<li class="toc-item toc-colophon"><div class="toc-title-box"><a href="backmatter-3.html" class="internal"><span class="title">Colophon</span></a></div></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul></nav></div>
|
||||
<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>
|
||||
|
||||
@@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false;
|
||||
eBookConfig.enableScratchAC = false;
|
||||
eBookConfig.build_info = "";
|
||||
eBookConfig.python3 = null;
|
||||
eBookConfig.runestone_version = '7.11.13';
|
||||
eBookConfig.runestone_version = '7.11.14';
|
||||
eBookConfig.jobehost = '';
|
||||
eBookConfig.proxyuri_runs = '';
|
||||
eBookConfig.proxyuri_files = '';
|
||||
eBookConfig.enable_chatcodes = false;
|
||||
</script>
|
||||
<!--*** Runestone Services ***-->
|
||||
<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
|
||||
<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">
|
||||
<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/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
|
||||
</script>
|
||||
@@ -146,6 +146,7 @@ eBookConfig.enable_chatcodes = false;
|
||||
\DeclareMathOperator{\Geom}{Geom}
|
||||
\DeclareMathOperator{\Poiss}{Poiss}
|
||||
\DeclareMathOperator{\Exp}{Exp}
|
||||
\DeclareMathOperator{\Norm}{N}
|
||||
|
||||
|
||||
\DeclareMathOperator{\E}{E}
|
||||
@@ -294,7 +295,16 @@ eBookConfig.enable_chatcodes = false;
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toc-item toc-backmatter"><div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div></li>
|
||||
<li class="toc-item toc-backmatter">
|
||||
<div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div>
|
||||
<ul class="structural toc-item-list">
|
||||
<li class="toc-item toc-appendix">
|
||||
<div class="toc-title-box"><a href="backmatter-2.html" class="internal"><span class="codenumber">A</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table</span></a></div>
|
||||
<ul class="structural toc-item-list"><li class="toc-item toc-section"><div class="toc-title-box"><a href="app-Phi-table.html" class="internal"><span class="codenumber">A.1</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table of Values</span></a></div></li></ul>
|
||||
</li>
|
||||
<li class="toc-item toc-colophon"><div class="toc-title-box"><a href="backmatter-3.html" class="internal"><span class="title">Colophon</span></a></div></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul></nav></div>
|
||||
<main class="ptx-main"><div id="ptx-content" class="ptx-content"><section class="chapter" id="ch-Hypothesis-Testing"><h2 class="heading">
|
||||
<span class="type">Chapter</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">5</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Hypothesis Testing</span>
|
||||
|
||||
+13
-3
@@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false;
|
||||
eBookConfig.enableScratchAC = false;
|
||||
eBookConfig.build_info = "";
|
||||
eBookConfig.python3 = null;
|
||||
eBookConfig.runestone_version = '7.11.13';
|
||||
eBookConfig.runestone_version = '7.11.14';
|
||||
eBookConfig.jobehost = '';
|
||||
eBookConfig.proxyuri_runs = '';
|
||||
eBookConfig.proxyuri_files = '';
|
||||
eBookConfig.enable_chatcodes = false;
|
||||
</script>
|
||||
<!--*** Runestone Services ***-->
|
||||
<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
|
||||
<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">
|
||||
<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/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
|
||||
</script>
|
||||
@@ -146,6 +146,7 @@ eBookConfig.enable_chatcodes = false;
|
||||
\DeclareMathOperator{\Geom}{Geom}
|
||||
\DeclareMathOperator{\Poiss}{Poiss}
|
||||
\DeclareMathOperator{\Exp}{Exp}
|
||||
\DeclareMathOperator{\Norm}{N}
|
||||
|
||||
|
||||
\DeclareMathOperator{\E}{E}
|
||||
@@ -294,7 +295,16 @@ eBookConfig.enable_chatcodes = false;
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toc-item toc-backmatter"><div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div></li>
|
||||
<li class="toc-item toc-backmatter">
|
||||
<div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div>
|
||||
<ul class="structural toc-item-list">
|
||||
<li class="toc-item toc-appendix">
|
||||
<div class="toc-title-box"><a href="backmatter-2.html" class="internal"><span class="codenumber">A</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table</span></a></div>
|
||||
<ul class="structural toc-item-list"><li class="toc-item toc-section"><div class="toc-title-box"><a href="app-Phi-table.html" class="internal"><span class="codenumber">A.1</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table of Values</span></a></div></li></ul>
|
||||
</li>
|
||||
<li class="toc-item toc-colophon"><div class="toc-title-box"><a href="backmatter-3.html" class="internal"><span class="title">Colophon</span></a></div></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul></nav></div>
|
||||
<main class="ptx-main"><div id="ptx-content" class="ptx-content"><section class="chapter" id="ch-Introduction"><h2 class="heading">
|
||||
<span class="type">Chapter</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">0</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Introduction</span>
|
||||
|
||||
@@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false;
|
||||
eBookConfig.enableScratchAC = false;
|
||||
eBookConfig.build_info = "";
|
||||
eBookConfig.python3 = null;
|
||||
eBookConfig.runestone_version = '7.11.13';
|
||||
eBookConfig.runestone_version = '7.11.14';
|
||||
eBookConfig.jobehost = '';
|
||||
eBookConfig.proxyuri_runs = '';
|
||||
eBookConfig.proxyuri_files = '';
|
||||
eBookConfig.enable_chatcodes = false;
|
||||
</script>
|
||||
<!--*** Runestone Services ***-->
|
||||
<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
|
||||
<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">
|
||||
<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/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
|
||||
</script>
|
||||
@@ -146,6 +146,7 @@ eBookConfig.enable_chatcodes = false;
|
||||
\DeclareMathOperator{\Geom}{Geom}
|
||||
\DeclareMathOperator{\Poiss}{Poiss}
|
||||
\DeclareMathOperator{\Exp}{Exp}
|
||||
\DeclareMathOperator{\Norm}{N}
|
||||
|
||||
|
||||
\DeclareMathOperator{\E}{E}
|
||||
@@ -294,7 +295,16 @@ eBookConfig.enable_chatcodes = false;
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toc-item toc-backmatter"><div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div></li>
|
||||
<li class="toc-item toc-backmatter">
|
||||
<div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div>
|
||||
<ul class="structural toc-item-list">
|
||||
<li class="toc-item toc-appendix">
|
||||
<div class="toc-title-box"><a href="backmatter-2.html" class="internal"><span class="codenumber">A</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table</span></a></div>
|
||||
<ul class="structural toc-item-list"><li class="toc-item toc-section"><div class="toc-title-box"><a href="app-Phi-table.html" class="internal"><span class="codenumber">A.1</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table of Values</span></a></div></li></ul>
|
||||
</li>
|
||||
<li class="toc-item toc-colophon"><div class="toc-title-box"><a href="backmatter-3.html" class="internal"><span class="title">Colophon</span></a></div></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul></nav></div>
|
||||
<main class="ptx-main"><div id="ptx-content" class="ptx-content"><section class="chapter" id="ch-Linear-Regression"><h2 class="heading">
|
||||
<span class="type">Chapter</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">6</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Linear Regression</span>
|
||||
|
||||
+13
-3
@@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false;
|
||||
eBookConfig.enableScratchAC = false;
|
||||
eBookConfig.build_info = "";
|
||||
eBookConfig.python3 = null;
|
||||
eBookConfig.runestone_version = '7.11.13';
|
||||
eBookConfig.runestone_version = '7.11.14';
|
||||
eBookConfig.jobehost = '';
|
||||
eBookConfig.proxyuri_runs = '';
|
||||
eBookConfig.proxyuri_files = '';
|
||||
eBookConfig.enable_chatcodes = false;
|
||||
</script>
|
||||
<!--*** Runestone Services ***-->
|
||||
<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
|
||||
<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">
|
||||
<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/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
|
||||
</script>
|
||||
@@ -146,6 +146,7 @@ eBookConfig.enable_chatcodes = false;
|
||||
\DeclareMathOperator{\Geom}{Geom}
|
||||
\DeclareMathOperator{\Poiss}{Poiss}
|
||||
\DeclareMathOperator{\Exp}{Exp}
|
||||
\DeclareMathOperator{\Norm}{N}
|
||||
|
||||
|
||||
\DeclareMathOperator{\E}{E}
|
||||
@@ -294,7 +295,16 @@ eBookConfig.enable_chatcodes = false;
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toc-item toc-backmatter"><div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div></li>
|
||||
<li class="toc-item toc-backmatter">
|
||||
<div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div>
|
||||
<ul class="structural toc-item-list">
|
||||
<li class="toc-item toc-appendix">
|
||||
<div class="toc-title-box"><a href="backmatter-2.html" class="internal"><span class="codenumber">A</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table</span></a></div>
|
||||
<ul class="structural toc-item-list"><li class="toc-item toc-section"><div class="toc-title-box"><a href="app-Phi-table.html" class="internal"><span class="codenumber">A.1</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table of Values</span></a></div></li></ul>
|
||||
</li>
|
||||
<li class="toc-item toc-colophon"><div class="toc-title-box"><a href="backmatter-3.html" class="internal"><span class="title">Colophon</span></a></div></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul></nav></div>
|
||||
<main class="ptx-main"><div id="ptx-content" class="ptx-content"><section class="chapter" id="ch-Probability"><h2 class="heading">
|
||||
<span class="type">Chapter</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">1</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Probability Theory</span>
|
||||
|
||||
@@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false;
|
||||
eBookConfig.enableScratchAC = false;
|
||||
eBookConfig.build_info = "";
|
||||
eBookConfig.python3 = null;
|
||||
eBookConfig.runestone_version = '7.11.13';
|
||||
eBookConfig.runestone_version = '7.11.14';
|
||||
eBookConfig.jobehost = '';
|
||||
eBookConfig.proxyuri_runs = '';
|
||||
eBookConfig.proxyuri_files = '';
|
||||
eBookConfig.enable_chatcodes = false;
|
||||
</script>
|
||||
<!--*** Runestone Services ***-->
|
||||
<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
|
||||
<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">
|
||||
<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/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
|
||||
</script>
|
||||
@@ -146,6 +146,7 @@ eBookConfig.enable_chatcodes = false;
|
||||
\DeclareMathOperator{\Geom}{Geom}
|
||||
\DeclareMathOperator{\Poiss}{Poiss}
|
||||
\DeclareMathOperator{\Exp}{Exp}
|
||||
\DeclareMathOperator{\Norm}{N}
|
||||
|
||||
|
||||
\DeclareMathOperator{\E}{E}
|
||||
@@ -294,7 +295,16 @@ eBookConfig.enable_chatcodes = false;
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toc-item toc-backmatter"><div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div></li>
|
||||
<li class="toc-item toc-backmatter">
|
||||
<div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div>
|
||||
<ul class="structural toc-item-list">
|
||||
<li class="toc-item toc-appendix">
|
||||
<div class="toc-title-box"><a href="backmatter-2.html" class="internal"><span class="codenumber">A</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table</span></a></div>
|
||||
<ul class="structural toc-item-list"><li class="toc-item toc-section"><div class="toc-title-box"><a href="app-Phi-table.html" class="internal"><span class="codenumber">A.1</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table of Values</span></a></div></li></ul>
|
||||
</li>
|
||||
<li class="toc-item toc-colophon"><div class="toc-title-box"><a href="backmatter-3.html" class="internal"><span class="title">Colophon</span></a></div></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul></nav></div>
|
||||
<main class="ptx-main"><div id="ptx-content" class="ptx-content"><section class="chapter" id="ch-Random-Variables"><h2 class="heading">
|
||||
<span class="type">Chapter</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">2</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Random Variables</span>
|
||||
|
||||
+13
-3
@@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false;
|
||||
eBookConfig.enableScratchAC = false;
|
||||
eBookConfig.build_info = "";
|
||||
eBookConfig.python3 = null;
|
||||
eBookConfig.runestone_version = '7.11.13';
|
||||
eBookConfig.runestone_version = '7.11.14';
|
||||
eBookConfig.jobehost = '';
|
||||
eBookConfig.proxyuri_runs = '';
|
||||
eBookConfig.proxyuri_files = '';
|
||||
eBookConfig.enable_chatcodes = false;
|
||||
</script>
|
||||
<!--*** Runestone Services ***-->
|
||||
<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
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<script src="_static/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">
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<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
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\DeclareMathOperator{\Poiss}{Poiss}
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\DeclareMathOperator{\Norm}{N}
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||||
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\DeclareMathOperator{\E}{E}
|
||||
@@ -294,7 +295,16 @@ eBookConfig.enable_chatcodes = false;
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toc-item toc-backmatter"><div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div></li>
|
||||
<li class="toc-item toc-backmatter">
|
||||
<div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div>
|
||||
<ul class="structural toc-item-list">
|
||||
<li class="toc-item toc-appendix">
|
||||
<div class="toc-title-box"><a href="backmatter-2.html" class="internal"><span class="codenumber">A</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table</span></a></div>
|
||||
<ul class="structural toc-item-list"><li class="toc-item toc-section"><div class="toc-title-box"><a href="app-Phi-table.html" class="internal"><span class="codenumber">A.1</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table of Values</span></a></div></li></ul>
|
||||
</li>
|
||||
<li class="toc-item toc-colophon"><div class="toc-title-box"><a href="backmatter-3.html" class="internal"><span class="title">Colophon</span></a></div></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul></nav></div>
|
||||
<main class="ptx-main"><div id="ptx-content" class="ptx-content"><section class="colophon" id="front-colophon"><h2 class="heading hide-type">
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<span class="type">Colophon</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">Colophon</span>
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||||
|
||||
+14
-4
@@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false;
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eBookConfig.enableScratchAC = false;
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eBookConfig.build_info = "";
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eBookConfig.python3 = null;
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eBookConfig.runestone_version = '7.11.14';
|
||||
eBookConfig.jobehost = '';
|
||||
eBookConfig.proxyuri_runs = '';
|
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eBookConfig.proxyuri_files = '';
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eBookConfig.enable_chatcodes = false;
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<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
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<script src="_static/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">
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<link rel="stylesheet" type="text/css" href="_static/prefix-runestone.6ec5960970d8b364.css">
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<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
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</script>
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@@ -146,6 +146,7 @@ eBookConfig.enable_chatcodes = false;
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\DeclareMathOperator{\Geom}{Geom}
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||||
\DeclareMathOperator{\Poiss}{Poiss}
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||||
\DeclareMathOperator{\Exp}{Exp}
|
||||
\DeclareMathOperator{\Norm}{N}
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|
||||
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\DeclareMathOperator{\E}{E}
|
||||
@@ -294,14 +295,23 @@ eBookConfig.enable_chatcodes = false;
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toc-item toc-backmatter"><div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div></li>
|
||||
<li class="toc-item toc-backmatter">
|
||||
<div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div>
|
||||
<ul class="structural toc-item-list">
|
||||
<li class="toc-item toc-appendix">
|
||||
<div class="toc-title-box"><a href="backmatter-2.html" class="internal"><span class="codenumber">A</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table</span></a></div>
|
||||
<ul class="structural toc-item-list"><li class="toc-item toc-section"><div class="toc-title-box"><a href="app-Phi-table.html" class="internal"><span class="codenumber">A.1</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table of Values</span></a></div></li></ul>
|
||||
</li>
|
||||
<li class="toc-item toc-colophon"><div class="toc-title-box"><a href="backmatter-3.html" class="internal"><span class="title">Colophon</span></a></div></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul></nav></div>
|
||||
<main class="ptx-main"><div id="ptx-content" class="ptx-content"><section class="frontmatter" id="frontmatter"><h2 class="heading"><span class="title">Math 1044 Notes</span></h2>
|
||||
<div class="author">
|
||||
<div class="author-name">Andy Eisenberg</div>
|
||||
<div class="author-info">Mathematics Department<br>Temple University</div>
|
||||
</div>
|
||||
<div class="date">February 10, 2026</div>
|
||||
<div class="date">February 19, 2026</div>
|
||||
<nav class="summary-links"><ul><li><a href="front-colophon.html" class="internal"><span class="title">Colophon</span></a></li></ul></nav><div class="autopermalink" data-description="Front Matter"><a href="#frontmatter" title="Copy heading and permalink for Front Matter" aria-label="Copy heading and permalink for Front Matter">🔗</a></div></section></div>
|
||||
<div id="ptx-content-footer" class="ptx-content-footer">
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||||
<a class="previous-button button" href="my-great-book.html" title="Previous"><span class="icon material-symbols-outlined" aria-hidden="true"></span><span class="name">Prev</span></a><a class="top-button button" href="#" title="Top"><span class="icon material-symbols-outlined" aria-hidden="true"></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"></span></a>
|
||||
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||||
+1
-1
@@ -2,7 +2,7 @@
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<meta name="robots" content="noindex, nofollow">
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</head>
|
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<body class="ignore-math">
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<article class="definition definition-like"><h4 class="heading">
|
||||
<span class="type">Definition</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">2.2.8</span><span class="period heading-divison-mark heading-divison-mark__period">.</span>
|
||||
</h4>
|
||||
<div class="para logical">
|
||||
<div class="para">Consider the parametrized family of functions:</div>
|
||||
<div class="displaymath process-math">
|
||||
\begin{gather*}
|
||||
f(x; \mu, \sigma^2) = \frac{1}{\sqrt{2\pi \sigma^2}} e^{\frac{-(x-\mu)^2}{2\sigma^2}}.
|
||||
\end{gather*}
|
||||
</div>
|
||||
<div class="para">The function <span class="process-math">\(f(x; \mu, \sigma^2)\)</span> is called a <dfn class="terminology">normal density function</dfn> with parameters <span class="process-math">\(\mu\)</span> and <span class="process-math">\(\sigma^2\text{.}\)</span> A continuous random variable <span class="process-math">\(X\)</span> with pdf <span class="process-math">\(f(x; \mu, \sigma^2)\)</span> is said to have a <dfn class="terminology">normal distribution</dfn>. We’ll write <span class="process-math">\(X \sim \Norm(\mu, \sigma^2)\text{.}\)</span>
|
||||
</div>
|
||||
<div class="autopermalink" data-description="Paragraph"><a href="#def-normal-distribution-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||||
</div> <div class="para">In the specific case that <span class="process-math">\(\mu = 0\)</span> and <span class="process-math">\(\sigma^2 = 1\text{,}\)</span> we call the resulting distribution the <dfn class="terminology">standard normal distribution</dfn>. We’ll use the notation <span class="process-math">\(\phi(x)\)</span> for the standard normal density function, and <span class="process-math">\(\Phi(x)\)</span> for the standard normal cumulative distribution function.<div class="autopermalink" data-description="Paragraph"><a href="#def-normal-distribution-1-2" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||||
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</body>
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</html>
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Executable
+44
@@ -0,0 +1,44 @@
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<!DOCTYPE html>
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<html lang="en-US" dir="ltr">
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<head>
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<meta name="robots" content="noindex, nofollow">
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||||
</head>
|
||||
<body class="ignore-math">
|
||||
<article class="theorem theorem-like"><h3 class="heading">
|
||||
<span class="type">Theorem</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.2.1</span><span class="period heading-divison-mark heading-divison-mark__period">.</span>
|
||||
</h3>
|
||||
<div class="para logical">
|
||||
<div class="para">Suppose <span class="process-math">\(X_1, X_2, \dotsc, X_n\)</span> are <dfn class="terminology">independent and identically distributed</dfn> (or <dfn class="terminology">iid</dfn>) random variables with finite expected value <span class="process-math">\(\mu\)</span> and finite variance <span class="process-math">\(\sigma^2\text{.}\)</span> Let:</div>
|
||||
<div class="displaymath process-math">
|
||||
\begin{align*}
|
||||
S_n \amp = X_1 + X_2 + \dotsb + X_n \\
|
||||
A_n \amp = \frac{X_1 + X_2 + \dotsb + X_n}{n}
|
||||
\end{align*}
|
||||
</div>
|
||||
<div class="para">Then, for sufficiently large <span class="process-math">\(n\text{:}\)</span>
|
||||
</div>
|
||||
<div class="displaymath process-math">
|
||||
\begin{gather*}
|
||||
S_n \approx \Norm(n \mu, n \sigma^2) \\
|
||||
A_n \approx \Norm\left(\mu, \frac{\sigma^2}{n}\right)
|
||||
\end{gather*}
|
||||
</div>
|
||||
<div class="autopermalink" data-description="Paragraph"><a href="#thm-CLT-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||||
</div>
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File diff suppressed because one or more lines are too long
+13
-3
@@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false;
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</script>
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\DeclareMathOperator{\Geom}{Geom}
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\DeclareMathOperator{\Poiss}{Poiss}
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\DeclareMathOperator{\Exp}{Exp}
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\DeclareMathOperator{\Norm}{N}
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\DeclareMathOperator{\E}{E}
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</li>
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</li>
|
||||
<li class="toc-item toc-backmatter"><div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div></li>
|
||||
<li class="toc-item toc-backmatter">
|
||||
<div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div>
|
||||
<ul class="structural toc-item-list">
|
||||
<li class="toc-item toc-appendix">
|
||||
<div class="toc-title-box"><a href="backmatter-2.html" class="internal"><span class="codenumber">A</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table</span></a></div>
|
||||
<ul class="structural toc-item-list"><li class="toc-item toc-section"><div class="toc-title-box"><a href="app-Phi-table.html" class="internal"><span class="codenumber">A.1</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table of Values</span></a></div></li></ul>
|
||||
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<li><a href="frontmatter.html" class="internal"><span class="title">Front Matter</span></a></li>
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+181
-6
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|
||||
<script src="_static/pretext/js/lti_iframe_resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min.js" integrity="sha512-4xUl/d6D6THrAnXAwGajXkoWaeMNwEKK4iNfq5DotEbLPAfk6FSxSP3ydNxqDgCw1c/0Z1Jg6L8h2j+++9BZmg==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><script src="lunr-pretext-search-index.js" async=""></script><script src="_static/pretext/js/pretext_search.js"></script><script src="_static/pretext/js/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
|
||||
</script>
|
||||
@@ -146,6 +146,7 @@ eBookConfig.enable_chatcodes = false;
|
||||
\DeclareMathOperator{\Geom}{Geom}
|
||||
\DeclareMathOperator{\Poiss}{Poiss}
|
||||
\DeclareMathOperator{\Exp}{Exp}
|
||||
\DeclareMathOperator{\Norm}{N}
|
||||
|
||||
|
||||
\DeclareMathOperator{\E}{E}
|
||||
@@ -294,12 +295,156 @@ eBookConfig.enable_chatcodes = false;
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toc-item toc-backmatter"><div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div></li>
|
||||
<li class="toc-item toc-backmatter">
|
||||
<div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div>
|
||||
<ul class="structural toc-item-list">
|
||||
<li class="toc-item toc-appendix">
|
||||
<div class="toc-title-box"><a href="backmatter-2.html" class="internal"><span class="codenumber">A</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table</span></a></div>
|
||||
<ul class="structural toc-item-list"><li class="toc-item toc-section"><div class="toc-title-box"><a href="app-Phi-table.html" class="internal"><span class="codenumber">A.1</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table of Values</span></a></div></li></ul>
|
||||
</li>
|
||||
<li class="toc-item toc-colophon"><div class="toc-title-box"><a href="backmatter-3.html" class="internal"><span class="title">Colophon</span></a></div></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul></nav></div>
|
||||
<main class="ptx-main"><div id="ptx-content" class="ptx-content"><section class="section" id="sec-CLT"><h2 class="heading hide-type">
|
||||
<span class="type">Section</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.2</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Central Limit Theorem</span>
|
||||
</h2>
|
||||
<div class="para" id="sec-CLT-2">Text of section.<div class="autopermalink" data-description="Paragraph"><a href="#sec-CLT-2" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||||
<div class="para" id="sec-CLT-2">Although we defined the normal distribution earlier (<a href="sec-Continuous-RVs.html#def-normal-distribution" class="xref" data-knowl="./knowl/xref/def-normal-distribution.html" data-reveal-label="Reveal" data-close-label="Close" title="Definition 2.2.8">Definition 2.2.8</a>), we haven’t done much in the way of probability calculations with it. The sense in which this distribution is "normal" is that it turns out other distributions, when added together or averaged, tend to be well-approximated by a normal distribution.<div class="autopermalink" data-description="Paragraph"><a href="#sec-CLT-2" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||||
</div>
|
||||
<article class="theorem theorem-like" id="thm-CLT"><h3 class="heading">
|
||||
<span class="type">Theorem</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.2.1</span><span class="period heading-divison-mark heading-divison-mark__period">.</span>
|
||||
</h3>
|
||||
<div class="para logical" id="thm-CLT-1-1">
|
||||
<div class="para">Suppose <span class="process-math">\(X_1, X_2, \dotsc, X_n\)</span> are <dfn class="terminology">independent and identically distributed</dfn> (or <dfn class="terminology">iid</dfn>) random variables with finite expected value <span class="process-math">\(\mu\)</span> and finite variance <span class="process-math">\(\sigma^2\text{.}\)</span> Let:</div>
|
||||
<div class="displaymath process-math" id="thm-CLT-1-1-6">
|
||||
\begin{align*}
|
||||
S_n \amp = X_1 + X_2 + \dotsb + X_n \\
|
||||
A_n \amp = \frac{X_1 + X_2 + \dotsb + X_n}{n}
|
||||
\end{align*}
|
||||
</div>
|
||||
<div class="para">Then, for sufficiently large <span class="process-math">\(n\text{:}\)</span>
|
||||
</div>
|
||||
<div class="displaymath process-math" id="thm-CLT-1-1-8">
|
||||
\begin{gather*}
|
||||
S_n \approx \Norm(n \mu, n \sigma^2) \\
|
||||
A_n \approx \Norm\left(\mu, \frac{\sigma^2}{n}\right)
|
||||
\end{gather*}
|
||||
</div>
|
||||
<div class="autopermalink" data-description="Paragraph"><a href="#thm-CLT-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="Theorem 4.2.1"><a href="#thm-CLT" title="Copy heading and permalink for Theorem 4.2.1" aria-label="Copy heading and permalink for Theorem 4.2.1">🔗</a></div></article><article class="remark remark-like" id="sec-CLT-4"><h3 class="heading">
|
||||
<span class="type">Remark</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.2.2</span><span class="period heading-divison-mark heading-divison-mark__period">.</span>
|
||||
</h3>
|
||||
<div class="para logical" id="sec-CLT-4-1">
|
||||
<div class="para">How large is "sufficiently large"? We’ll make use of two common rules of thumb:</div>
|
||||
<ol class="decimal" id="sec-CLT-4-1-1"><li id="sec-CLT-4-1-1-1">
|
||||
<div class="para" id="sec-CLT-4-1-1-1-1">For general distributions, we’d like <span class="process-math">\(n \geq 30\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#sec-CLT-4-1-1-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||||
</div>
|
||||
<div class="autopermalink" data-description="Item 1"><a href="#sec-CLT-4-1-1-1" title="Copy heading and permalink for Item 1" aria-label="Copy heading and permalink for Item 1">🔗</a></div>
|
||||
</li></ol>
|
||||
<ol class="decimal" id="sec-CLT-4-1-2"><li id="sec-CLT-4-1-2-1">
|
||||
<div class="para" id="sec-CLT-4-1-2-1-1">For a binomial distribution specifically, we’d like <span class="process-math">\(n\)</span> large enough that we have at least five heads and five tails.<div class="autopermalink" data-description="Paragraph"><a href="#sec-CLT-4-1-2-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||||
</div>
|
||||
<div class="autopermalink" data-description="Item 1"><a href="#sec-CLT-4-1-2-1" title="Copy heading and permalink for Item 1" aria-label="Copy heading and permalink for Item 1">🔗</a></div>
|
||||
</li></ol>
|
||||
<div class="autopermalink" data-description="Paragraph"><a href="#sec-CLT-4-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||||
</div>
|
||||
<div class="autopermalink" data-description="Remark 4.2.2"><a href="#sec-CLT-4" title="Copy heading and permalink for Remark 4.2.2" aria-label="Copy heading and permalink for Remark 4.2.2">🔗</a></div></article><div class="para logical" id="sec-CLT-5">
|
||||
<div class="para">When a normal distribution gets translated and/or scaled, the result is another normal distribution. It will often be useful to <em class="emphasis">standardize</em> a normal distribution <span class="process-math">\(X = \Norm(\mu, \sigma^2)\)</span> as follows:</div>
|
||||
<div class="displaymath process-math" id="sec-CLT-5-3">
|
||||
\begin{gather*}
|
||||
Z = \frac{X - \mu}{\sigma} = \Norm(0, 1).
|
||||
\end{gather*}
|
||||
</div>
|
||||
<div class="para">Given an <span class="process-math">\(X\)</span>-value <span class="process-math">\(a\text{,}\)</span> the corresponding value of <span class="process-math">\(Z\)</span> is called a <dfn class="terminology"><span class="process-math">\(z\)</span>-score</dfn>, and is sometimes denoted <span class="process-math">\(a^*\)</span>
|
||||
</div>
|
||||
<div class="autopermalink" data-description="Paragraph"><a href="#sec-CLT-5" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||||
</div>
|
||||
<article class="example example-like" id="sec-CLT-6"><h3 class="heading">
|
||||
<span class="type">Example</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.2.3</span><span class="period heading-divison-mark heading-divison-mark__period">.</span>
|
||||
</h3>
|
||||
<div class="para logical" id="sec-CLT-6-1-1">
|
||||
<div class="para">Suppose we flip a fair coin 100 times and let <span class="process-math">\(S_{100}\)</span> be the number of heads. In order to calculate, for example, <span class="process-math">\(\Pr(40 \leq S_{100} \leq 60)\)</span> using the binomial distribution probability formula, we would need to calculate:</div>
|
||||
<div class="displaymath process-math" data-contains-math-knowls="./knowl/xref/thm-CLT.html" id="sec-CLT-6-1-1-3">
|
||||
\begin{gather*}
|
||||
\Pr(40 \leq S_{100} \leq 60) = \sum_{k = 40}^{60} {100 \choose k} (0.5)^k (1 - 0.5)^{100 - k}.
|
||||
\end{gather*}
|
||||
</div>
|
||||
<div class="para">This could be done using a good calculator. If we increased the number of flips to 1000, or 10000, etc., even a powerful calculator might struggle with the computation. However, if we’re willing to accept an approximation, then <a href="sec-CLT.html#thm-CLT" class="xref" data-knowl="./knowl/xref/thm-CLT.html" data-reveal-label="Reveal" data-close-label="Close" title="Theorem 4.2.1">Theorem 4.2.1</a> gives a (mostly) straightforward path:</div>
|
||||
<div class="displaymath process-math" data-contains-math-knowls="./knowl/xref/thm-CLT.html" id="sec-CLT-6-1-1-5">
|
||||
\begin{align*}
|
||||
\E(S_{100}) \amp = np = (100)(0.5) = 50 \\
|
||||
\Var(S_{100}) \amp = np(1-p) = (100)(0.5)(0.5) = 25 \\
|
||||
\Rightarrow \quad S_{100} \amp\approx \Norm(50, 25) \\
|
||||
Z \amp = \frac{S_{100} - 50}{\sqrt{25}} \\
|
||||
\Pr(40 \leq S_{100} \leq 60) \amp\approx \Pr\left(\frac{40 - 50}{5} \leq Z \leq \frac{60 - 50}{5}\right) \\
|
||||
\amp= \Pr\left(-2 \leq Z \leq 2\right)
|
||||
\end{align*}
|
||||
</div>
|
||||
<div class="para">We now reach a potential impass.</div>
|
||||
<div class="autopermalink" data-description="Paragraph"><a href="#sec-CLT-6-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||||
</div>
|
||||
<div class="autopermalink" data-description="Example 4.2.3"><a href="#sec-CLT-6" title="Copy heading and permalink for Example 4.2.3" aria-label="Copy heading and permalink for Example 4.2.3">🔗</a></div></article><div class="para logical" id="sec-CLT-7">
|
||||
<div class="para">The random variable <span class="process-math">\(Z\)</span> is the <em class="emphasis">standard normal distribution</em>, with pdf:</div>
|
||||
<div class="displaymath process-math" id="sec-CLT-7-3">
|
||||
\begin{gather*}
|
||||
\phi(x) = \frac{1}{\sqrt{2\pi}} e^{-x^2/2}
|
||||
\end{gather*}
|
||||
</div>
|
||||
<div class="para">To calculate probabilities like <span class="process-math">\(\Pr(-2 \leq Z \leq 2)\text{,}\)</span> we should evaluate the integral:</div>
|
||||
<div class="displaymath process-math" id="sec-CLT-7-5">
|
||||
\begin{gather*}
|
||||
\Pr(-2 \leq Z \leq 2) = \int_{-2}^2 \phi(x)\ dx = \int_{-2}^2 \frac{1}{\sqrt{2\pi}} e^{-x^2/2}\ dx
|
||||
\end{gather*}
|
||||
</div>
|
||||
<div class="para">Alternatively, we could use the cdf:</div>
|
||||
<div class="displaymath process-math" id="sec-CLT-7-6">
|
||||
\begin{gather*}
|
||||
\Phi(x) = \int_{-\infty}^x \phi(t)\ dt = \int_{-\infty}^x \frac{1}{\sqrt{2\pi}} e^{-t^2/2}\ dt
|
||||
\end{gather*}
|
||||
</div>
|
||||
<div class="para">If we had a nice formula for <span class="process-math">\(\Phi(x)\text{,}\)</span> then we could complete the probability calculation:</div>
|
||||
<div class="displaymath process-math" id="sec-CLT-7-8">
|
||||
\begin{gather*}
|
||||
\Pr(-2\leq Z \leq 2) = \Phi(2) - \Phi(-2).
|
||||
\end{gather*}
|
||||
</div>
|
||||
<div class="para">Unfortunately, we don’t have a nice formula for <span class="process-math">\(\Phi(x)\text{.}\)</span> In fact, there is provably no "nice" formula that could be written for <span class="process-math">\(\Phi(x)\)</span> (where "nice" has some technical mathematical meaning that we won’t discuss here).</div>
|
||||
<div class="autopermalink" data-description="Paragraph"><a href="#sec-CLT-7" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||||
</div>
|
||||
<div class="para" id="sec-CLT-8">The true power of <a href="sec-CLT.html#thm-CLT" class="xref" data-knowl="./knowl/xref/thm-CLT.html" data-reveal-label="Reveal" data-close-label="Close" title="Theorem 4.2.1">Theorem 4.2.1</a> comes to the rescue: it doesn’t matter what type of distribution the individual <span class="process-math">\(X_i\)</span>’s have, and it doesn’t matter what type of distributions <span class="process-math">\(S_n\)</span> and <span class="process-math">\(A_n\)</span> have. The random variable <span class="process-math">\(Z\)</span> is <span class="process-math">\(\Norm(0, 1)\text{.}\)</span> Since it’s the same particular distribution all the time, and since we’re only aiming at an approximation anyway, we can calculate many estimations of probabilities like <span class="process-math">\(\Pr(a \leq Z \leq b)\)</span> ahead of time and just save the results to look up later.<div class="autopermalink" data-description="Paragraph"><a href="#sec-CLT-8" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||||
</div>
|
||||
<div class="para" id="sec-CLT-9">A table of precalculated <span class="process-math">\(\Phi(z)\)</span> values can be found in <a href="app-Phi-table.html" class="internal" title="Section A.1: \Phi(z) Table of Values">Section A.1</a>.<div class="autopermalink" data-description="Paragraph"><a href="#sec-CLT-9" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||||
</div>
|
||||
<article class="example example-like" id="sec-CLT-10"><h3 class="heading">
|
||||
<span class="type">Example</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.2.4</span><span class="period heading-divison-mark heading-divison-mark__period">.</span>
|
||||
</h3>
|
||||
<div class="para logical" id="sec-CLT-10-1-1">
|
||||
<div class="para">Continuing the previous example, and having looked up the values <span class="process-math">\(\Phi(2) \approx 0.9772\)</span> and <span class="process-math">\(\Phi(-2) \approx 0.0228\text{,}\)</span> we complete our estimation:</div>
|
||||
<div class="displaymath process-math" id="sec-CLT-10-1-1-3">
|
||||
\begin{align*}
|
||||
\Pr(40 \leq S_{100} \leq 60) \amp\approx \Pr\left(\frac{40 - 50}{5} \leq Z \leq \frac{60 - 50}{5}\right) \\
|
||||
\amp= \Pr\left(-2 \leq Z \leq 2\right) \\
|
||||
\amp \approx \Phi(2) - \Phi(-2) \\
|
||||
\amp \approx 0.9772 - 0.0228 \\
|
||||
\amp = 0.9544.
|
||||
\end{align*}
|
||||
</div>
|
||||
<div class="autopermalink" data-description="Paragraph"><a href="#sec-CLT-10-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||||
</div>
|
||||
<div class="autopermalink" data-description="Example 4.2.4"><a href="#sec-CLT-10" title="Copy heading and permalink for Example 4.2.4" aria-label="Copy heading and permalink for Example 4.2.4">🔗</a></div></article><div class="para logical" id="sec-CLT-11">
|
||||
<div class="para">The true value is approximately <span class="process-math">\(0.965\text{,}\)</span> so we underestimated the probability a bit. It turns out this will consistently be the case when using a normal approximation to a discrete distribution, such as the binomial distribution. The range of values <span class="process-math">\(40 \leq S_{100} \leq 60\)</span> is a list of <span class="process-math">\(21\)</span> discrete values. However, the continuous interval <span class="process-math">\([40, 60]\)</span> has a length of only 20. So calculating the <span class="process-math">\(z\)</span>-scores from the values <span class="process-math">\(40\)</span> and <span class="process-math">\(60\)</span> has the effect of shortening the interval length by 1. To mitigate this, we can make a <dfn class="terminology">continuity correction</dfn> by extending the values out by <span class="process-math">\(0.5\)</span> in each direction:</div>
|
||||
<div class="displaymath process-math" id="sec-CLT-11-10">
|
||||
\begin{align*}
|
||||
\Pr(40 \leq S_{100} \leq 60) \amp\approx \Pr\left(\frac{39.5 - 50}{5} \leq Z \leq \frac{60.5 - 50}{5}\right) \\
|
||||
\amp= \Pr\left(-2.1 \leq Z \leq 2.1\right) \\
|
||||
\amp \approx \Phi(2.1) - \Phi(-2.1) \\
|
||||
\amp \approx 0.9821 - 0.0179 \\
|
||||
\amp = 0.9642.
|
||||
\end{align*}
|
||||
</div>
|
||||
<div class="para">This is a much more accurate estimate.</div>
|
||||
<div class="autopermalink" data-description="Paragraph"><a href="#sec-CLT-11" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||||
</div>
|
||||
<section class="exercises" id="exercises-CLT"><h3 class="heading hide-type">
|
||||
<span class="type">Exercises</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber"></span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Exercises</span>
|
||||
@@ -307,21 +452,51 @@ eBookConfig.enable_chatcodes = false;
|
||||
<article class="exercise exercise-like" id="exercises-CLT-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-CLT-1-1-1">Suppose a coin has probability 0.4 of coming up heads, and we flip the coin 100 times. Let <span class="process-math">\(S\)</span> be the number of heads. Estimate the probability that <span class="process-math">\(34 \leq S \leq 44\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-CLT-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-CLT-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-CLT-1-2-1">
|
||||
<span class="process-math">\(\Pr(34 \leq S \leq 44) \approx 0.8212 - 0.0918 = 0.7294.\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-CLT-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 4.2.1.1"><a href="#exercises-CLT-1-2" title="Copy heading and permalink for Answer 4.2.1.1" aria-label="Copy heading and permalink for Answer 4.2.1.1">🔗</a></div>
|
||||
</div></details></div>
|
||||
<div class="autopermalink" data-description="Exercise 4.2.1"><a href="#exercises-CLT-1" title="Copy heading and permalink for Exercise 4.2.1" aria-label="Copy heading and permalink for Exercise 4.2.1">🔗</a></div></article><article class="exercise exercise-like" id="exercises-CLT-2"><h4 class="heading"><span class="codenumber">2<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
|
||||
<div class="para" id="exercises-CLT-2-1-1">Suppose a fair die is rolled 100 times, and let <span class="process-math">\(m\)</span> be the average value of the rolls. Estimate the probability that <span class="process-math">\(3.45 \leq m \leq 3.55\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-CLT-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-CLT-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-CLT-2-2-1">
|
||||
<span class="process-math">\(\Pr(3.45 \leq m \leq 3.55) \approx 0.6141 - 0.3859 = 0.2282.\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-CLT-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 4.2.2.1"><a href="#exercises-CLT-2-2" title="Copy heading and permalink for Answer 4.2.2.1" aria-label="Copy heading and permalink for Answer 4.2.2.1">🔗</a></div>
|
||||
</div></details></div>
|
||||
<div class="autopermalink" data-description="Exercise 4.2.2"><a href="#exercises-CLT-2" title="Copy heading and permalink for Exercise 4.2.2" aria-label="Copy heading and permalink for Exercise 4.2.2">🔗</a></div></article><article class="exercise exercise-like" id="exercises-CLT-3"><h4 class="heading"><span class="codenumber">3<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
|
||||
<div class="introduction" id="exercises-CLT-3-1"><div class="para" id="exercises-CLT-3-1-1">The heights of men in the US have a mean of 69 in and a variance of about 9 in<span class="process-math">\(^2\text{,}\)</span> and the heights of women in the US have a mean of 63.5 in with a variance of 6.25 in<span class="process-math">\(^2\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-CLT-3-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||||
</div></div>
|
||||
<article class="task exercise-like" id="exercises-CLT-3-2"><h5 class="heading"><span class="codenumber">(a)</span></h5>
|
||||
<div class="para" id="exercises-CLT-3-2-1-1">Suppose the heights of 30 men are sampled, and a sample mean <span class="process-math">\(m\)</span> is taken. Find the expected value and variance of <span class="process-math">\(m\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-CLT-3-2-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||||
</div>
|
||||
<div class="solutions"><details id="exercises-CLT-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-CLT-3-2-2-1">
|
||||
<span class="process-math">\(\E(m) = 69\)</span> and <span class="process-math">\(\Var(m) = 0.3\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-CLT-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 4.2.3.a.1"><a href="#exercises-CLT-3-2-2" title="Copy heading and permalink for Answer 4.2.3.a.1" aria-label="Copy heading and permalink for Answer 4.2.3.a.1">🔗</a></div>
|
||||
</div></details></div>
|
||||
<div class="autopermalink" data-description="Task 4.2.3.a"><a href="#exercises-CLT-3-2" title="Copy heading and permalink for Task 4.2.3.a" aria-label="Copy heading and permalink for Task 4.2.3.a">🔗</a></div></article><article class="task exercise-like" id="exercises-CLT-3-3"><h5 class="heading"><span class="codenumber">(b)</span></h5>
|
||||
<div class="para" id="exercises-CLT-3-3-1-1">Estimate the probability that <span class="process-math">\(m \geq 69.5\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-CLT-3-3-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||||
</div>
|
||||
<div class="autopermalink" data-description="Task 4.2.3.b"><a href="#exercises-CLT-3-3" title="Copy heading and permalink for Task 4.2.3.b" aria-label="Copy heading and permalink for Task 4.2.3.b">🔗</a></div></article><article class="task exercise-like" id="exercises-CLT-3-4"><h5 class="heading"><span class="codenumber">(c)</span></h5>
|
||||
<div class="para" id="exercises-CLT-3-4-1-1">What if the sampled group was women?<div class="autopermalink" data-description="Paragraph"><a href="#exercises-CLT-3-4-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||||
<div class="solutions"><details id="exercises-CLT-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-CLT-3-3-2-1">
|
||||
<span class="process-math">\(\Pr(m \geq 69.5) \approx 1 - 0.8186 = 0.1814\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-CLT-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 4.2.3.b.1"><a href="#exercises-CLT-3-3-2" title="Copy heading and permalink for Answer 4.2.3.b.1" aria-label="Copy heading and permalink for Answer 4.2.3.b.1">🔗</a></div>
|
||||
</div></details></div>
|
||||
<div class="autopermalink" data-description="Task 4.2.3.b"><a href="#exercises-CLT-3-3" title="Copy heading and permalink for Task 4.2.3.b" aria-label="Copy heading and permalink for Task 4.2.3.b">🔗</a></div></article><article class="task exercise-like" id="exercises-CLT-3-4"><h5 class="heading"><span class="codenumber">(c)</span></h5>
|
||||
<div class="para" id="exercises-CLT-3-4-1-1">If the sampled group was women, estimate the probability that <span class="process-math">\(m \geq 64\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-CLT-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-CLT-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-CLT-3-4-2-1">
|
||||
<span class="process-math">\(\E(m) = 63.5\)</span> and <span class="process-math">\(\Var(m) \approx 0.208\text{.}\)</span> <span class="process-math">\(\Pr(m \geq 64) \approx 1 - 0.8643 = 0.1357\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-CLT-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 4.2.3.c.1"><a href="#exercises-CLT-3-4-2" title="Copy heading and permalink for Answer 4.2.3.c.1" aria-label="Copy heading and permalink for Answer 4.2.3.c.1">🔗</a></div>
|
||||
</div></details></div>
|
||||
<div class="autopermalink" data-description="Task 4.2.3.c"><a href="#exercises-CLT-3-4" title="Copy heading and permalink for Task 4.2.3.c" aria-label="Copy heading and permalink for Task 4.2.3.c">🔗</a></div></article><div class="autopermalink" data-description="Exercise 4.2.3"><a href="#exercises-CLT-3" title="Copy heading and permalink for Exercise 4.2.3" aria-label="Copy heading and permalink for Exercise 4.2.3">🔗</a></div></article><div class="autopermalink" data-description="Exercises 4.2"><a href="#exercises-CLT" title="Copy heading and permalink for Exercises 4.2" aria-label="Copy heading and permalink for Exercises 4.2">🔗</a></div></section><div class="autopermalink" data-description="Section 4.2: Central Limit Theorem"><a href="#sec-CLT" title="Copy heading and permalink for Section 4.2: Central Limit Theorem" aria-label="Copy heading and permalink for Section 4.2: Central Limit Theorem">🔗</a></div></section></div>
|
||||
<div id="ptx-content-footer" class="ptx-content-footer">
|
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<a class="previous-button button" href="sec-Likelihood.html" title="Previous"><span class="icon material-symbols-outlined" aria-hidden="true"></span><span class="name">Prev</span></a><a class="top-button button" href="#" title="Top"><span class="icon material-symbols-outlined" aria-hidden="true"></span><span class="name">Top</span></a><a class="next-button button" href="sec-Confidence-Intervals.html" title="Next"><span class="name">Next</span><span class="icon material-symbols-outlined" aria-hidden="true"></span></a>
|
||||
|
||||
+13
-3
@@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false;
|
||||
eBookConfig.enableScratchAC = false;
|
||||
eBookConfig.build_info = "";
|
||||
eBookConfig.python3 = null;
|
||||
eBookConfig.runestone_version = '7.11.13';
|
||||
eBookConfig.runestone_version = '7.11.14';
|
||||
eBookConfig.jobehost = '';
|
||||
eBookConfig.proxyuri_runs = '';
|
||||
eBookConfig.proxyuri_files = '';
|
||||
eBookConfig.enable_chatcodes = false;
|
||||
</script>
|
||||
<!--*** Runestone Services ***-->
|
||||
<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
|
||||
<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">
|
||||
<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/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
|
||||
</script>
|
||||
@@ -146,6 +146,7 @@ eBookConfig.enable_chatcodes = false;
|
||||
\DeclareMathOperator{\Geom}{Geom}
|
||||
\DeclareMathOperator{\Poiss}{Poiss}
|
||||
\DeclareMathOperator{\Exp}{Exp}
|
||||
\DeclareMathOperator{\Norm}{N}
|
||||
|
||||
|
||||
\DeclareMathOperator{\E}{E}
|
||||
@@ -294,7 +295,16 @@ eBookConfig.enable_chatcodes = false;
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toc-item toc-backmatter"><div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div></li>
|
||||
<li class="toc-item toc-backmatter">
|
||||
<div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div>
|
||||
<ul class="structural toc-item-list">
|
||||
<li class="toc-item toc-appendix">
|
||||
<div class="toc-title-box"><a href="backmatter-2.html" class="internal"><span class="codenumber">A</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table</span></a></div>
|
||||
<ul class="structural toc-item-list"><li class="toc-item toc-section"><div class="toc-title-box"><a href="app-Phi-table.html" class="internal"><span class="codenumber">A.1</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table of Values</span></a></div></li></ul>
|
||||
</li>
|
||||
<li class="toc-item toc-colophon"><div class="toc-title-box"><a href="backmatter-3.html" class="internal"><span class="title">Colophon</span></a></div></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul></nav></div>
|
||||
<main class="ptx-main"><div id="ptx-content" class="ptx-content"><section class="section" id="sec-Chi-Squared"><h2 class="heading hide-type">
|
||||
<span class="type">Section</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">5.4</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title"><span class="process-math">\(\chi^2\)</span> Test</span>
|
||||
|
||||
@@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false;
|
||||
eBookConfig.enableScratchAC = false;
|
||||
eBookConfig.build_info = "";
|
||||
eBookConfig.python3 = null;
|
||||
eBookConfig.runestone_version = '7.11.13';
|
||||
eBookConfig.runestone_version = '7.11.14';
|
||||
eBookConfig.jobehost = '';
|
||||
eBookConfig.proxyuri_runs = '';
|
||||
eBookConfig.proxyuri_files = '';
|
||||
eBookConfig.enable_chatcodes = false;
|
||||
</script>
|
||||
<!--*** Runestone Services ***-->
|
||||
<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
|
||||
<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">
|
||||
<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/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
|
||||
</script>
|
||||
@@ -146,6 +146,7 @@ eBookConfig.enable_chatcodes = false;
|
||||
\DeclareMathOperator{\Geom}{Geom}
|
||||
\DeclareMathOperator{\Poiss}{Poiss}
|
||||
\DeclareMathOperator{\Exp}{Exp}
|
||||
\DeclareMathOperator{\Norm}{N}
|
||||
|
||||
|
||||
\DeclareMathOperator{\E}{E}
|
||||
@@ -294,7 +295,16 @@ eBookConfig.enable_chatcodes = false;
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toc-item toc-backmatter"><div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div></li>
|
||||
<li class="toc-item toc-backmatter">
|
||||
<div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div>
|
||||
<ul class="structural toc-item-list">
|
||||
<li class="toc-item toc-appendix">
|
||||
<div class="toc-title-box"><a href="backmatter-2.html" class="internal"><span class="codenumber">A</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table</span></a></div>
|
||||
<ul class="structural toc-item-list"><li class="toc-item toc-section"><div class="toc-title-box"><a href="app-Phi-table.html" class="internal"><span class="codenumber">A.1</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table of Values</span></a></div></li></ul>
|
||||
</li>
|
||||
<li class="toc-item toc-colophon"><div class="toc-title-box"><a href="backmatter-3.html" class="internal"><span class="title">Colophon</span></a></div></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul></nav></div>
|
||||
<main class="ptx-main"><div id="ptx-content" class="ptx-content"><section class="section" id="sec-Conditional-Probability"><h2 class="heading hide-type">
|
||||
<span class="type">Section</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">1.3</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Conditional Probability</span>
|
||||
|
||||
@@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false;
|
||||
eBookConfig.enableScratchAC = false;
|
||||
eBookConfig.build_info = "";
|
||||
eBookConfig.python3 = null;
|
||||
eBookConfig.runestone_version = '7.11.13';
|
||||
eBookConfig.runestone_version = '7.11.14';
|
||||
eBookConfig.jobehost = '';
|
||||
eBookConfig.proxyuri_runs = '';
|
||||
eBookConfig.proxyuri_files = '';
|
||||
eBookConfig.enable_chatcodes = false;
|
||||
</script>
|
||||
<!--*** Runestone Services ***-->
|
||||
<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
|
||||
<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">
|
||||
<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/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
|
||||
</script>
|
||||
@@ -146,6 +146,7 @@ eBookConfig.enable_chatcodes = false;
|
||||
\DeclareMathOperator{\Geom}{Geom}
|
||||
\DeclareMathOperator{\Poiss}{Poiss}
|
||||
\DeclareMathOperator{\Exp}{Exp}
|
||||
\DeclareMathOperator{\Norm}{N}
|
||||
|
||||
|
||||
\DeclareMathOperator{\E}{E}
|
||||
@@ -294,7 +295,16 @@ eBookConfig.enable_chatcodes = false;
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toc-item toc-backmatter"><div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div></li>
|
||||
<li class="toc-item toc-backmatter">
|
||||
<div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div>
|
||||
<ul class="structural toc-item-list">
|
||||
<li class="toc-item toc-appendix">
|
||||
<div class="toc-title-box"><a href="backmatter-2.html" class="internal"><span class="codenumber">A</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table</span></a></div>
|
||||
<ul class="structural toc-item-list"><li class="toc-item toc-section"><div class="toc-title-box"><a href="app-Phi-table.html" class="internal"><span class="codenumber">A.1</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table of Values</span></a></div></li></ul>
|
||||
</li>
|
||||
<li class="toc-item toc-colophon"><div class="toc-title-box"><a href="backmatter-3.html" class="internal"><span class="title">Colophon</span></a></div></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul></nav></div>
|
||||
<main class="ptx-main"><div id="ptx-content" class="ptx-content"><section class="section" id="sec-Confidence-Intervals"><h2 class="heading hide-type">
|
||||
<span class="type">Section</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.3</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Confidence Intervals</span>
|
||||
|
||||
+16
-4
@@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false;
|
||||
eBookConfig.enableScratchAC = false;
|
||||
eBookConfig.build_info = "";
|
||||
eBookConfig.python3 = null;
|
||||
eBookConfig.runestone_version = '7.11.13';
|
||||
eBookConfig.runestone_version = '7.11.14';
|
||||
eBookConfig.jobehost = '';
|
||||
eBookConfig.proxyuri_runs = '';
|
||||
eBookConfig.proxyuri_files = '';
|
||||
eBookConfig.enable_chatcodes = false;
|
||||
</script>
|
||||
<!--*** Runestone Services ***-->
|
||||
<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
|
||||
<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">
|
||||
<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/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
|
||||
</script>
|
||||
@@ -146,6 +146,7 @@ eBookConfig.enable_chatcodes = false;
|
||||
\DeclareMathOperator{\Geom}{Geom}
|
||||
\DeclareMathOperator{\Poiss}{Poiss}
|
||||
\DeclareMathOperator{\Exp}{Exp}
|
||||
\DeclareMathOperator{\Norm}{N}
|
||||
|
||||
|
||||
\DeclareMathOperator{\E}{E}
|
||||
@@ -294,7 +295,16 @@ eBookConfig.enable_chatcodes = false;
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toc-item toc-backmatter"><div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div></li>
|
||||
<li class="toc-item toc-backmatter">
|
||||
<div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div>
|
||||
<ul class="structural toc-item-list">
|
||||
<li class="toc-item toc-appendix">
|
||||
<div class="toc-title-box"><a href="backmatter-2.html" class="internal"><span class="codenumber">A</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table</span></a></div>
|
||||
<ul class="structural toc-item-list"><li class="toc-item toc-section"><div class="toc-title-box"><a href="app-Phi-table.html" class="internal"><span class="codenumber">A.1</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table of Values</span></a></div></li></ul>
|
||||
</li>
|
||||
<li class="toc-item toc-colophon"><div class="toc-title-box"><a href="backmatter-3.html" class="internal"><span class="title">Colophon</span></a></div></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul></nav></div>
|
||||
<main class="ptx-main"><div id="ptx-content" class="ptx-content"><section class="section" id="sec-Continuous-RVs"><h2 class="heading hide-type">
|
||||
<span class="type">Section</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">2.2</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Continuous Random Variables</span>
|
||||
@@ -529,8 +539,10 @@ f(t) = \lambda e^{-\lambda t}
|
||||
f(x; \mu, \sigma^2) = \frac{1}{\sqrt{2\pi \sigma^2}} e^{\frac{-(x-\mu)^2}{2\sigma^2}}.
|
||||
\end{gather*}
|
||||
</div>
|
||||
<div class="para">The function <span class="process-math">\(f(x; \mu, \sigma^2)\)</span> is called a <dfn class="terminology">normal density function</dfn> with parameters <span class="process-math">\(\mu\)</span> and <span class="process-math">\(\sigma^2\text{.}\)</span> A continuous random variable <span class="process-math">\(X\)</span> with pdf <span class="process-math">\(f(x; \mu, \sigma^2)\)</span> is said to have a <dfn class="terminology">normal distribution</dfn>. In the specific case that <span class="process-math">\(\mu = 0\)</span> and <span class="process-math">\(\sigma^2 = 1\text{,}\)</span> we call the resulting distribution the <dfn class="terminology">standard normal distribution</dfn>.</div>
|
||||
<div class="para">The function <span class="process-math">\(f(x; \mu, \sigma^2)\)</span> is called a <dfn class="terminology">normal density function</dfn> with parameters <span class="process-math">\(\mu\)</span> and <span class="process-math">\(\sigma^2\text{.}\)</span> A continuous random variable <span class="process-math">\(X\)</span> with pdf <span class="process-math">\(f(x; \mu, \sigma^2)\)</span> is said to have a <dfn class="terminology">normal distribution</dfn>. We’ll write <span class="process-math">\(X \sim \Norm(\mu, \sigma^2)\text{.}\)</span>
|
||||
</div>
|
||||
<div class="autopermalink" data-description="Paragraph"><a href="#def-normal-distribution-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||||
</div> <div class="para" id="def-normal-distribution-1-2">In the specific case that <span class="process-math">\(\mu = 0\)</span> and <span class="process-math">\(\sigma^2 = 1\text{,}\)</span> we call the resulting distribution the <dfn class="terminology">standard normal distribution</dfn>. We’ll use the notation <span class="process-math">\(\phi(x)\)</span> for the standard normal density function, and <span class="process-math">\(\Phi(x)\)</span> for the standard normal cumulative distribution function.<div class="autopermalink" data-description="Paragraph"><a href="#def-normal-distribution-1-2" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||||
</div>
|
||||
<div class="autopermalink" data-description="Definition 2.2.8"><a href="#def-normal-distribution" title="Copy heading and permalink for Definition 2.2.8" aria-label="Copy heading and permalink for Definition 2.2.8">🔗</a></div></article><div class="para" id="subsec-normal-distribution-3">It’s an unfortunate reality that the normal density functions can’t easily be integrated. (In fact, it is provably impossible to write nice formulas for their antiderivatives). So we won’t worry much about probability computations like <span class="process-math">\(\Pr(c \leq X \leq d)\)</span> for normal distributions. The normal distributions will play a <em class="emphasis">central</em> role in later chapters (after which you can return here and appreciate this pun).<div class="autopermalink" data-description="Paragraph"><a href="#subsec-normal-distribution-3" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||||
</div>
|
||||
|
||||
+13
-3
@@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false;
|
||||
eBookConfig.enableScratchAC = false;
|
||||
eBookConfig.build_info = "";
|
||||
eBookConfig.python3 = null;
|
||||
eBookConfig.runestone_version = '7.11.13';
|
||||
eBookConfig.runestone_version = '7.11.14';
|
||||
eBookConfig.jobehost = '';
|
||||
eBookConfig.proxyuri_runs = '';
|
||||
eBookConfig.proxyuri_files = '';
|
||||
eBookConfig.enable_chatcodes = false;
|
||||
</script>
|
||||
<!--*** Runestone Services ***-->
|
||||
<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
|
||||
<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">
|
||||
<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/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
|
||||
</script>
|
||||
@@ -146,6 +146,7 @@ eBookConfig.enable_chatcodes = false;
|
||||
\DeclareMathOperator{\Geom}{Geom}
|
||||
\DeclareMathOperator{\Poiss}{Poiss}
|
||||
\DeclareMathOperator{\Exp}{Exp}
|
||||
\DeclareMathOperator{\Norm}{N}
|
||||
|
||||
|
||||
\DeclareMathOperator{\E}{E}
|
||||
@@ -294,7 +295,16 @@ eBookConfig.enable_chatcodes = false;
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toc-item toc-backmatter"><div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div></li>
|
||||
<li class="toc-item toc-backmatter">
|
||||
<div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div>
|
||||
<ul class="structural toc-item-list">
|
||||
<li class="toc-item toc-appendix">
|
||||
<div class="toc-title-box"><a href="backmatter-2.html" class="internal"><span class="codenumber">A</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table</span></a></div>
|
||||
<ul class="structural toc-item-list"><li class="toc-item toc-section"><div class="toc-title-box"><a href="app-Phi-table.html" class="internal"><span class="codenumber">A.1</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table of Values</span></a></div></li></ul>
|
||||
</li>
|
||||
<li class="toc-item toc-colophon"><div class="toc-title-box"><a href="backmatter-3.html" class="internal"><span class="title">Colophon</span></a></div></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul></nav></div>
|
||||
<main class="ptx-main"><div id="ptx-content" class="ptx-content"><section class="section" id="sec-Correlation"><h2 class="heading hide-type">
|
||||
<span class="type">Section</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">6.1</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Correlation</span>
|
||||
|
||||
+13
-3
@@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false;
|
||||
eBookConfig.enableScratchAC = false;
|
||||
eBookConfig.build_info = "";
|
||||
eBookConfig.python3 = null;
|
||||
eBookConfig.runestone_version = '7.11.13';
|
||||
eBookConfig.runestone_version = '7.11.14';
|
||||
eBookConfig.jobehost = '';
|
||||
eBookConfig.proxyuri_runs = '';
|
||||
eBookConfig.proxyuri_files = '';
|
||||
eBookConfig.enable_chatcodes = false;
|
||||
</script>
|
||||
<!--*** Runestone Services ***-->
|
||||
<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
|
||||
<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">
|
||||
<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/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
|
||||
</script>
|
||||
@@ -146,6 +146,7 @@ eBookConfig.enable_chatcodes = false;
|
||||
\DeclareMathOperator{\Geom}{Geom}
|
||||
\DeclareMathOperator{\Poiss}{Poiss}
|
||||
\DeclareMathOperator{\Exp}{Exp}
|
||||
\DeclareMathOperator{\Norm}{N}
|
||||
|
||||
|
||||
\DeclareMathOperator{\E}{E}
|
||||
@@ -294,7 +295,16 @@ eBookConfig.enable_chatcodes = false;
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toc-item toc-backmatter"><div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div></li>
|
||||
<li class="toc-item toc-backmatter">
|
||||
<div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div>
|
||||
<ul class="structural toc-item-list">
|
||||
<li class="toc-item toc-appendix">
|
||||
<div class="toc-title-box"><a href="backmatter-2.html" class="internal"><span class="codenumber">A</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table</span></a></div>
|
||||
<ul class="structural toc-item-list"><li class="toc-item toc-section"><div class="toc-title-box"><a href="app-Phi-table.html" class="internal"><span class="codenumber">A.1</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table of Values</span></a></div></li></ul>
|
||||
</li>
|
||||
<li class="toc-item toc-colophon"><div class="toc-title-box"><a href="backmatter-3.html" class="internal"><span class="title">Colophon</span></a></div></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul></nav></div>
|
||||
<main class="ptx-main"><div id="ptx-content" class="ptx-content"><section class="section" id="sec-Covariance"><h2 class="heading hide-type">
|
||||
<span class="type">Section</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">3.3</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Covariance</span>
|
||||
|
||||
+13
-3
@@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false;
|
||||
eBookConfig.enableScratchAC = false;
|
||||
eBookConfig.build_info = "";
|
||||
eBookConfig.python3 = null;
|
||||
eBookConfig.runestone_version = '7.11.13';
|
||||
eBookConfig.runestone_version = '7.11.14';
|
||||
eBookConfig.jobehost = '';
|
||||
eBookConfig.proxyuri_runs = '';
|
||||
eBookConfig.proxyuri_files = '';
|
||||
eBookConfig.enable_chatcodes = false;
|
||||
</script>
|
||||
<!--*** Runestone Services ***-->
|
||||
<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
|
||||
<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">
|
||||
<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/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
|
||||
</script>
|
||||
@@ -146,6 +146,7 @@ eBookConfig.enable_chatcodes = false;
|
||||
\DeclareMathOperator{\Geom}{Geom}
|
||||
\DeclareMathOperator{\Poiss}{Poiss}
|
||||
\DeclareMathOperator{\Exp}{Exp}
|
||||
\DeclareMathOperator{\Norm}{N}
|
||||
|
||||
|
||||
\DeclareMathOperator{\E}{E}
|
||||
@@ -294,7 +295,16 @@ eBookConfig.enable_chatcodes = false;
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toc-item toc-backmatter"><div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div></li>
|
||||
<li class="toc-item toc-backmatter">
|
||||
<div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div>
|
||||
<ul class="structural toc-item-list">
|
||||
<li class="toc-item toc-appendix">
|
||||
<div class="toc-title-box"><a href="backmatter-2.html" class="internal"><span class="codenumber">A</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table</span></a></div>
|
||||
<ul class="structural toc-item-list"><li class="toc-item toc-section"><div class="toc-title-box"><a href="app-Phi-table.html" class="internal"><span class="codenumber">A.1</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table of Values</span></a></div></li></ul>
|
||||
</li>
|
||||
<li class="toc-item toc-colophon"><div class="toc-title-box"><a href="backmatter-3.html" class="internal"><span class="title">Colophon</span></a></div></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul></nav></div>
|
||||
<main class="ptx-main"><div id="ptx-content" class="ptx-content"><section class="section" id="sec-Discrete-RVs"><h2 class="heading hide-type">
|
||||
<span class="type">Section</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">2.1</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Discrete Random Variables</span>
|
||||
|
||||
+13
-3
@@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false;
|
||||
eBookConfig.enableScratchAC = false;
|
||||
eBookConfig.build_info = "";
|
||||
eBookConfig.python3 = null;
|
||||
eBookConfig.runestone_version = '7.11.13';
|
||||
eBookConfig.runestone_version = '7.11.14';
|
||||
eBookConfig.jobehost = '';
|
||||
eBookConfig.proxyuri_runs = '';
|
||||
eBookConfig.proxyuri_files = '';
|
||||
eBookConfig.enable_chatcodes = false;
|
||||
</script>
|
||||
<!--*** Runestone Services ***-->
|
||||
<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
|
||||
<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">
|
||||
<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/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
|
||||
</script>
|
||||
@@ -146,6 +146,7 @@ eBookConfig.enable_chatcodes = false;
|
||||
\DeclareMathOperator{\Geom}{Geom}
|
||||
\DeclareMathOperator{\Poiss}{Poiss}
|
||||
\DeclareMathOperator{\Exp}{Exp}
|
||||
\DeclareMathOperator{\Norm}{N}
|
||||
|
||||
|
||||
\DeclareMathOperator{\E}{E}
|
||||
@@ -294,7 +295,16 @@ eBookConfig.enable_chatcodes = false;
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toc-item toc-backmatter"><div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div></li>
|
||||
<li class="toc-item toc-backmatter">
|
||||
<div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div>
|
||||
<ul class="structural toc-item-list">
|
||||
<li class="toc-item toc-appendix">
|
||||
<div class="toc-title-box"><a href="backmatter-2.html" class="internal"><span class="codenumber">A</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table</span></a></div>
|
||||
<ul class="structural toc-item-list"><li class="toc-item toc-section"><div class="toc-title-box"><a href="app-Phi-table.html" class="internal"><span class="codenumber">A.1</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table of Values</span></a></div></li></ul>
|
||||
</li>
|
||||
<li class="toc-item toc-colophon"><div class="toc-title-box"><a href="backmatter-3.html" class="internal"><span class="title">Colophon</span></a></div></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul></nav></div>
|
||||
<main class="ptx-main"><div id="ptx-content" class="ptx-content"><section class="section" id="sec-Expected-Value"><h2 class="heading hide-type">
|
||||
<span class="type">Section</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">3.1</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Expected Value</span>
|
||||
|
||||
@@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false;
|
||||
eBookConfig.enableScratchAC = false;
|
||||
eBookConfig.build_info = "";
|
||||
eBookConfig.python3 = null;
|
||||
eBookConfig.runestone_version = '7.11.13';
|
||||
eBookConfig.runestone_version = '7.11.14';
|
||||
eBookConfig.jobehost = '';
|
||||
eBookConfig.proxyuri_runs = '';
|
||||
eBookConfig.proxyuri_files = '';
|
||||
eBookConfig.enable_chatcodes = false;
|
||||
</script>
|
||||
<!--*** Runestone Services ***-->
|
||||
<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
|
||||
<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">
|
||||
<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/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
|
||||
</script>
|
||||
@@ -146,6 +146,7 @@ eBookConfig.enable_chatcodes = false;
|
||||
\DeclareMathOperator{\Geom}{Geom}
|
||||
\DeclareMathOperator{\Poiss}{Poiss}
|
||||
\DeclareMathOperator{\Exp}{Exp}
|
||||
\DeclareMathOperator{\Norm}{N}
|
||||
|
||||
|
||||
\DeclareMathOperator{\E}{E}
|
||||
@@ -294,7 +295,16 @@ eBookConfig.enable_chatcodes = false;
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toc-item toc-backmatter"><div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div></li>
|
||||
<li class="toc-item toc-backmatter">
|
||||
<div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div>
|
||||
<ul class="structural toc-item-list">
|
||||
<li class="toc-item toc-appendix">
|
||||
<div class="toc-title-box"><a href="backmatter-2.html" class="internal"><span class="codenumber">A</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table</span></a></div>
|
||||
<ul class="structural toc-item-list"><li class="toc-item toc-section"><div class="toc-title-box"><a href="app-Phi-table.html" class="internal"><span class="codenumber">A.1</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table of Values</span></a></div></li></ul>
|
||||
</li>
|
||||
<li class="toc-item toc-colophon"><div class="toc-title-box"><a href="backmatter-3.html" class="internal"><span class="title">Colophon</span></a></div></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul></nav></div>
|
||||
<main class="ptx-main"><div id="ptx-content" class="ptx-content"><section class="section" id="sec-Independent-Events"><h2 class="heading hide-type">
|
||||
<span class="type">Section</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">1.4</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Independent Events</span>
|
||||
|
||||
+13
-3
@@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false;
|
||||
eBookConfig.enableScratchAC = false;
|
||||
eBookConfig.build_info = "";
|
||||
eBookConfig.python3 = null;
|
||||
eBookConfig.runestone_version = '7.11.13';
|
||||
eBookConfig.runestone_version = '7.11.14';
|
||||
eBookConfig.jobehost = '';
|
||||
eBookConfig.proxyuri_runs = '';
|
||||
eBookConfig.proxyuri_files = '';
|
||||
eBookConfig.enable_chatcodes = false;
|
||||
</script>
|
||||
<!--*** Runestone Services ***-->
|
||||
<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
|
||||
<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">
|
||||
<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/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
|
||||
</script>
|
||||
@@ -146,6 +146,7 @@ eBookConfig.enable_chatcodes = false;
|
||||
\DeclareMathOperator{\Geom}{Geom}
|
||||
\DeclareMathOperator{\Poiss}{Poiss}
|
||||
\DeclareMathOperator{\Exp}{Exp}
|
||||
\DeclareMathOperator{\Norm}{N}
|
||||
|
||||
|
||||
\DeclareMathOperator{\E}{E}
|
||||
@@ -294,7 +295,16 @@ eBookConfig.enable_chatcodes = false;
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toc-item toc-backmatter"><div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div></li>
|
||||
<li class="toc-item toc-backmatter">
|
||||
<div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div>
|
||||
<ul class="structural toc-item-list">
|
||||
<li class="toc-item toc-appendix">
|
||||
<div class="toc-title-box"><a href="backmatter-2.html" class="internal"><span class="codenumber">A</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table</span></a></div>
|
||||
<ul class="structural toc-item-list"><li class="toc-item toc-section"><div class="toc-title-box"><a href="app-Phi-table.html" class="internal"><span class="codenumber">A.1</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table of Values</span></a></div></li></ul>
|
||||
</li>
|
||||
<li class="toc-item toc-colophon"><div class="toc-title-box"><a href="backmatter-3.html" class="internal"><span class="title">Colophon</span></a></div></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul></nav></div>
|
||||
<main class="ptx-main"><div id="ptx-content" class="ptx-content"><section class="section" id="sec-Introduction"><h2 class="heading hide-type">
|
||||
<span class="type">Section</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">0.1</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Introduction</span>
|
||||
|
||||
@@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false;
|
||||
eBookConfig.enableScratchAC = false;
|
||||
eBookConfig.build_info = "";
|
||||
eBookConfig.python3 = null;
|
||||
eBookConfig.runestone_version = '7.11.13';
|
||||
eBookConfig.runestone_version = '7.11.14';
|
||||
eBookConfig.jobehost = '';
|
||||
eBookConfig.proxyuri_runs = '';
|
||||
eBookConfig.proxyuri_files = '';
|
||||
eBookConfig.enable_chatcodes = false;
|
||||
</script>
|
||||
<!--*** Runestone Services ***-->
|
||||
<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
|
||||
<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">
|
||||
<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/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
|
||||
</script>
|
||||
@@ -146,6 +146,7 @@ eBookConfig.enable_chatcodes = false;
|
||||
\DeclareMathOperator{\Geom}{Geom}
|
||||
\DeclareMathOperator{\Poiss}{Poiss}
|
||||
\DeclareMathOperator{\Exp}{Exp}
|
||||
\DeclareMathOperator{\Norm}{N}
|
||||
|
||||
|
||||
\DeclareMathOperator{\E}{E}
|
||||
@@ -294,7 +295,16 @@ eBookConfig.enable_chatcodes = false;
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toc-item toc-backmatter"><div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div></li>
|
||||
<li class="toc-item toc-backmatter">
|
||||
<div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div>
|
||||
<ul class="structural toc-item-list">
|
||||
<li class="toc-item toc-appendix">
|
||||
<div class="toc-title-box"><a href="backmatter-2.html" class="internal"><span class="codenumber">A</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table</span></a></div>
|
||||
<ul class="structural toc-item-list"><li class="toc-item toc-section"><div class="toc-title-box"><a href="app-Phi-table.html" class="internal"><span class="codenumber">A.1</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table of Values</span></a></div></li></ul>
|
||||
</li>
|
||||
<li class="toc-item toc-colophon"><div class="toc-title-box"><a href="backmatter-3.html" class="internal"><span class="title">Colophon</span></a></div></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul></nav></div>
|
||||
<main class="ptx-main"><div id="ptx-content" class="ptx-content"><section class="section" id="sec-Joint-Distributions"><h2 class="heading hide-type">
|
||||
<span class="type">Section</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">2.3</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Joint Distributions</span>
|
||||
|
||||
+13
-3
@@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false;
|
||||
eBookConfig.enableScratchAC = false;
|
||||
eBookConfig.build_info = "";
|
||||
eBookConfig.python3 = null;
|
||||
eBookConfig.runestone_version = '7.11.13';
|
||||
eBookConfig.runestone_version = '7.11.14';
|
||||
eBookConfig.jobehost = '';
|
||||
eBookConfig.proxyuri_runs = '';
|
||||
eBookConfig.proxyuri_files = '';
|
||||
eBookConfig.enable_chatcodes = false;
|
||||
</script>
|
||||
<!--*** Runestone Services ***-->
|
||||
<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
|
||||
<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">
|
||||
<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/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
|
||||
</script>
|
||||
@@ -146,6 +146,7 @@ eBookConfig.enable_chatcodes = false;
|
||||
\DeclareMathOperator{\Geom}{Geom}
|
||||
\DeclareMathOperator{\Poiss}{Poiss}
|
||||
\DeclareMathOperator{\Exp}{Exp}
|
||||
\DeclareMathOperator{\Norm}{N}
|
||||
|
||||
|
||||
\DeclareMathOperator{\E}{E}
|
||||
@@ -294,7 +295,16 @@ eBookConfig.enable_chatcodes = false;
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toc-item toc-backmatter"><div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div></li>
|
||||
<li class="toc-item toc-backmatter">
|
||||
<div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div>
|
||||
<ul class="structural toc-item-list">
|
||||
<li class="toc-item toc-appendix">
|
||||
<div class="toc-title-box"><a href="backmatter-2.html" class="internal"><span class="codenumber">A</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table</span></a></div>
|
||||
<ul class="structural toc-item-list"><li class="toc-item toc-section"><div class="toc-title-box"><a href="app-Phi-table.html" class="internal"><span class="codenumber">A.1</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table of Values</span></a></div></li></ul>
|
||||
</li>
|
||||
<li class="toc-item toc-colophon"><div class="toc-title-box"><a href="backmatter-3.html" class="internal"><span class="title">Colophon</span></a></div></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul></nav></div>
|
||||
<main class="ptx-main"><div id="ptx-content" class="ptx-content"><section class="section" id="sec-Likelihood"><h2 class="heading hide-type">
|
||||
<span class="type">Section</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.1</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Likelihood</span>
|
||||
|
||||
@@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false;
|
||||
eBookConfig.enableScratchAC = false;
|
||||
eBookConfig.build_info = "";
|
||||
eBookConfig.python3 = null;
|
||||
eBookConfig.runestone_version = '7.11.13';
|
||||
eBookConfig.runestone_version = '7.11.14';
|
||||
eBookConfig.jobehost = '';
|
||||
eBookConfig.proxyuri_runs = '';
|
||||
eBookConfig.proxyuri_files = '';
|
||||
eBookConfig.enable_chatcodes = false;
|
||||
</script>
|
||||
<!--*** Runestone Services ***-->
|
||||
<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
|
||||
<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">
|
||||
<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/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
|
||||
</script>
|
||||
@@ -146,6 +146,7 @@ eBookConfig.enable_chatcodes = false;
|
||||
\DeclareMathOperator{\Geom}{Geom}
|
||||
\DeclareMathOperator{\Poiss}{Poiss}
|
||||
\DeclareMathOperator{\Exp}{Exp}
|
||||
\DeclareMathOperator{\Norm}{N}
|
||||
|
||||
|
||||
\DeclareMathOperator{\E}{E}
|
||||
@@ -294,7 +295,16 @@ eBookConfig.enable_chatcodes = false;
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toc-item toc-backmatter"><div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div></li>
|
||||
<li class="toc-item toc-backmatter">
|
||||
<div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div>
|
||||
<ul class="structural toc-item-list">
|
||||
<li class="toc-item toc-appendix">
|
||||
<div class="toc-title-box"><a href="backmatter-2.html" class="internal"><span class="codenumber">A</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table</span></a></div>
|
||||
<ul class="structural toc-item-list"><li class="toc-item toc-section"><div class="toc-title-box"><a href="app-Phi-table.html" class="internal"><span class="codenumber">A.1</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table of Values</span></a></div></li></ul>
|
||||
</li>
|
||||
<li class="toc-item toc-colophon"><div class="toc-title-box"><a href="backmatter-3.html" class="internal"><span class="title">Colophon</span></a></div></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul></nav></div>
|
||||
<main class="ptx-main"><div id="ptx-content" class="ptx-content"><section class="section" id="sec-Linear-Regression"><h2 class="heading hide-type">
|
||||
<span class="type">Section</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">6.2</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Linear Regression</span>
|
||||
|
||||
@@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false;
|
||||
eBookConfig.enableScratchAC = false;
|
||||
eBookConfig.build_info = "";
|
||||
eBookConfig.python3 = null;
|
||||
eBookConfig.runestone_version = '7.11.13';
|
||||
eBookConfig.runestone_version = '7.11.14';
|
||||
eBookConfig.jobehost = '';
|
||||
eBookConfig.proxyuri_runs = '';
|
||||
eBookConfig.proxyuri_files = '';
|
||||
eBookConfig.enable_chatcodes = false;
|
||||
</script>
|
||||
<!--*** Runestone Services ***-->
|
||||
<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
|
||||
<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">
|
||||
<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/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
|
||||
</script>
|
||||
@@ -146,6 +146,7 @@ eBookConfig.enable_chatcodes = false;
|
||||
\DeclareMathOperator{\Geom}{Geom}
|
||||
\DeclareMathOperator{\Poiss}{Poiss}
|
||||
\DeclareMathOperator{\Exp}{Exp}
|
||||
\DeclareMathOperator{\Norm}{N}
|
||||
|
||||
|
||||
\DeclareMathOperator{\E}{E}
|
||||
@@ -294,7 +295,16 @@ eBookConfig.enable_chatcodes = false;
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toc-item toc-backmatter"><div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div></li>
|
||||
<li class="toc-item toc-backmatter">
|
||||
<div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div>
|
||||
<ul class="structural toc-item-list">
|
||||
<li class="toc-item toc-appendix">
|
||||
<div class="toc-title-box"><a href="backmatter-2.html" class="internal"><span class="codenumber">A</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table</span></a></div>
|
||||
<ul class="structural toc-item-list"><li class="toc-item toc-section"><div class="toc-title-box"><a href="app-Phi-table.html" class="internal"><span class="codenumber">A.1</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table of Values</span></a></div></li></ul>
|
||||
</li>
|
||||
<li class="toc-item toc-colophon"><div class="toc-title-box"><a href="backmatter-3.html" class="internal"><span class="title">Colophon</span></a></div></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul></nav></div>
|
||||
<main class="ptx-main"><div id="ptx-content" class="ptx-content"><section class="section" id="sec-One-Sample-Tests"><h2 class="heading hide-type">
|
||||
<span class="type">Section</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">5.1</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">One Sample Tests</span>
|
||||
|
||||
+13
-3
@@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false;
|
||||
eBookConfig.enableScratchAC = false;
|
||||
eBookConfig.build_info = "";
|
||||
eBookConfig.python3 = null;
|
||||
eBookConfig.runestone_version = '7.11.13';
|
||||
eBookConfig.runestone_version = '7.11.14';
|
||||
eBookConfig.jobehost = '';
|
||||
eBookConfig.proxyuri_runs = '';
|
||||
eBookConfig.proxyuri_files = '';
|
||||
eBookConfig.enable_chatcodes = false;
|
||||
</script>
|
||||
<!--*** Runestone Services ***-->
|
||||
<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
|
||||
<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">
|
||||
<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/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
|
||||
</script>
|
||||
@@ -146,6 +146,7 @@ eBookConfig.enable_chatcodes = false;
|
||||
\DeclareMathOperator{\Geom}{Geom}
|
||||
\DeclareMathOperator{\Poiss}{Poiss}
|
||||
\DeclareMathOperator{\Exp}{Exp}
|
||||
\DeclareMathOperator{\Norm}{N}
|
||||
|
||||
|
||||
\DeclareMathOperator{\E}{E}
|
||||
@@ -294,7 +295,16 @@ eBookConfig.enable_chatcodes = false;
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toc-item toc-backmatter"><div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div></li>
|
||||
<li class="toc-item toc-backmatter">
|
||||
<div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div>
|
||||
<ul class="structural toc-item-list">
|
||||
<li class="toc-item toc-appendix">
|
||||
<div class="toc-title-box"><a href="backmatter-2.html" class="internal"><span class="codenumber">A</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table</span></a></div>
|
||||
<ul class="structural toc-item-list"><li class="toc-item toc-section"><div class="toc-title-box"><a href="app-Phi-table.html" class="internal"><span class="codenumber">A.1</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table of Values</span></a></div></li></ul>
|
||||
</li>
|
||||
<li class="toc-item toc-colophon"><div class="toc-title-box"><a href="backmatter-3.html" class="internal"><span class="title">Colophon</span></a></div></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul></nav></div>
|
||||
<main class="ptx-main"><div id="ptx-content" class="ptx-content"><section class="section" id="sec-Power"><h2 class="heading hide-type">
|
||||
<span class="type">Section</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">5.3</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Power of a Test</span>
|
||||
|
||||
+13
-3
@@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false;
|
||||
eBookConfig.enableScratchAC = false;
|
||||
eBookConfig.build_info = "";
|
||||
eBookConfig.python3 = null;
|
||||
eBookConfig.runestone_version = '7.11.13';
|
||||
eBookConfig.runestone_version = '7.11.14';
|
||||
eBookConfig.jobehost = '';
|
||||
eBookConfig.proxyuri_runs = '';
|
||||
eBookConfig.proxyuri_files = '';
|
||||
eBookConfig.enable_chatcodes = false;
|
||||
</script>
|
||||
<!--*** Runestone Services ***-->
|
||||
<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
|
||||
<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">
|
||||
<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/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
|
||||
</script>
|
||||
@@ -146,6 +146,7 @@ eBookConfig.enable_chatcodes = false;
|
||||
\DeclareMathOperator{\Geom}{Geom}
|
||||
\DeclareMathOperator{\Poiss}{Poiss}
|
||||
\DeclareMathOperator{\Exp}{Exp}
|
||||
\DeclareMathOperator{\Norm}{N}
|
||||
|
||||
|
||||
\DeclareMathOperator{\E}{E}
|
||||
@@ -294,7 +295,16 @@ eBookConfig.enable_chatcodes = false;
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toc-item toc-backmatter"><div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div></li>
|
||||
<li class="toc-item toc-backmatter">
|
||||
<div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div>
|
||||
<ul class="structural toc-item-list">
|
||||
<li class="toc-item toc-appendix">
|
||||
<div class="toc-title-box"><a href="backmatter-2.html" class="internal"><span class="codenumber">A</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table</span></a></div>
|
||||
<ul class="structural toc-item-list"><li class="toc-item toc-section"><div class="toc-title-box"><a href="app-Phi-table.html" class="internal"><span class="codenumber">A.1</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table of Values</span></a></div></li></ul>
|
||||
</li>
|
||||
<li class="toc-item toc-colophon"><div class="toc-title-box"><a href="backmatter-3.html" class="internal"><span class="title">Colophon</span></a></div></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul></nav></div>
|
||||
<main class="ptx-main"><div id="ptx-content" class="ptx-content"><section class="section" id="sec-Probability"><h2 class="heading hide-type">
|
||||
<span class="type">Section</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">1.2</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Definition of Probability</span>
|
||||
|
||||
+13
-3
@@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false;
|
||||
eBookConfig.enableScratchAC = false;
|
||||
eBookConfig.build_info = "";
|
||||
eBookConfig.python3 = null;
|
||||
eBookConfig.runestone_version = '7.11.13';
|
||||
eBookConfig.runestone_version = '7.11.14';
|
||||
eBookConfig.jobehost = '';
|
||||
eBookConfig.proxyuri_runs = '';
|
||||
eBookConfig.proxyuri_files = '';
|
||||
eBookConfig.enable_chatcodes = false;
|
||||
</script>
|
||||
<!--*** Runestone Services ***-->
|
||||
<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
|
||||
<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">
|
||||
<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/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
|
||||
</script>
|
||||
@@ -146,6 +146,7 @@ eBookConfig.enable_chatcodes = false;
|
||||
\DeclareMathOperator{\Geom}{Geom}
|
||||
\DeclareMathOperator{\Poiss}{Poiss}
|
||||
\DeclareMathOperator{\Exp}{Exp}
|
||||
\DeclareMathOperator{\Norm}{N}
|
||||
|
||||
|
||||
\DeclareMathOperator{\E}{E}
|
||||
@@ -294,7 +295,16 @@ eBookConfig.enable_chatcodes = false;
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toc-item toc-backmatter"><div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div></li>
|
||||
<li class="toc-item toc-backmatter">
|
||||
<div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div>
|
||||
<ul class="structural toc-item-list">
|
||||
<li class="toc-item toc-appendix">
|
||||
<div class="toc-title-box"><a href="backmatter-2.html" class="internal"><span class="codenumber">A</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table</span></a></div>
|
||||
<ul class="structural toc-item-list"><li class="toc-item toc-section"><div class="toc-title-box"><a href="app-Phi-table.html" class="internal"><span class="codenumber">A.1</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table of Values</span></a></div></li></ul>
|
||||
</li>
|
||||
<li class="toc-item toc-colophon"><div class="toc-title-box"><a href="backmatter-3.html" class="internal"><span class="title">Colophon</span></a></div></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul></nav></div>
|
||||
<main class="ptx-main"><div id="ptx-content" class="ptx-content"><section class="section" id="sec-Set-Theory"><h2 class="heading hide-type">
|
||||
<span class="type">Section</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">1.1</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Set Theory</span>
|
||||
|
||||
@@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false;
|
||||
eBookConfig.enableScratchAC = false;
|
||||
eBookConfig.build_info = "";
|
||||
eBookConfig.python3 = null;
|
||||
eBookConfig.runestone_version = '7.11.13';
|
||||
eBookConfig.runestone_version = '7.11.14';
|
||||
eBookConfig.jobehost = '';
|
||||
eBookConfig.proxyuri_runs = '';
|
||||
eBookConfig.proxyuri_files = '';
|
||||
eBookConfig.enable_chatcodes = false;
|
||||
</script>
|
||||
<!--*** Runestone Services ***-->
|
||||
<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
|
||||
<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">
|
||||
<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/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
|
||||
</script>
|
||||
@@ -146,6 +146,7 @@ eBookConfig.enable_chatcodes = false;
|
||||
\DeclareMathOperator{\Geom}{Geom}
|
||||
\DeclareMathOperator{\Poiss}{Poiss}
|
||||
\DeclareMathOperator{\Exp}{Exp}
|
||||
\DeclareMathOperator{\Norm}{N}
|
||||
|
||||
|
||||
\DeclareMathOperator{\E}{E}
|
||||
@@ -294,7 +295,16 @@ eBookConfig.enable_chatcodes = false;
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toc-item toc-backmatter"><div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div></li>
|
||||
<li class="toc-item toc-backmatter">
|
||||
<div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div>
|
||||
<ul class="structural toc-item-list">
|
||||
<li class="toc-item toc-appendix">
|
||||
<div class="toc-title-box"><a href="backmatter-2.html" class="internal"><span class="codenumber">A</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table</span></a></div>
|
||||
<ul class="structural toc-item-list"><li class="toc-item toc-section"><div class="toc-title-box"><a href="app-Phi-table.html" class="internal"><span class="codenumber">A.1</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table of Values</span></a></div></li></ul>
|
||||
</li>
|
||||
<li class="toc-item toc-colophon"><div class="toc-title-box"><a href="backmatter-3.html" class="internal"><span class="title">Colophon</span></a></div></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul></nav></div>
|
||||
<main class="ptx-main"><div id="ptx-content" class="ptx-content"><section class="section" id="sec-Two-Sample-Tests"><h2 class="heading hide-type">
|
||||
<span class="type">Section</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">5.2</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Two Sample Tests</span>
|
||||
|
||||
+13
-3
@@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false;
|
||||
eBookConfig.enableScratchAC = false;
|
||||
eBookConfig.build_info = "";
|
||||
eBookConfig.python3 = null;
|
||||
eBookConfig.runestone_version = '7.11.13';
|
||||
eBookConfig.runestone_version = '7.11.14';
|
||||
eBookConfig.jobehost = '';
|
||||
eBookConfig.proxyuri_runs = '';
|
||||
eBookConfig.proxyuri_files = '';
|
||||
eBookConfig.enable_chatcodes = false;
|
||||
</script>
|
||||
<!--*** Runestone Services ***-->
|
||||
<script src="_static/prefix-runtime.0d5f811896ddeac1.bundle.js"></script><script src="_static/prefix-723.3e6434f80549315a.bundle.js"></script><script src="_static/prefix-runestone.e2abc79debce15fd.bundle.js"></script><link rel="stylesheet" type="text/css" href="_static/prefix-723.3bccd435914aa0ff.css">
|
||||
<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">
|
||||
<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/knowl.js"></script><!--knowl.js code controls Sage Cells within knowls--><script>sagecellEvalName='Evaluate (Sage)';
|
||||
</script>
|
||||
@@ -146,6 +146,7 @@ eBookConfig.enable_chatcodes = false;
|
||||
\DeclareMathOperator{\Geom}{Geom}
|
||||
\DeclareMathOperator{\Poiss}{Poiss}
|
||||
\DeclareMathOperator{\Exp}{Exp}
|
||||
\DeclareMathOperator{\Norm}{N}
|
||||
|
||||
|
||||
\DeclareMathOperator{\E}{E}
|
||||
@@ -294,7 +295,16 @@ eBookConfig.enable_chatcodes = false;
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toc-item toc-backmatter"><div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div></li>
|
||||
<li class="toc-item toc-backmatter">
|
||||
<div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div>
|
||||
<ul class="structural toc-item-list">
|
||||
<li class="toc-item toc-appendix">
|
||||
<div class="toc-title-box"><a href="backmatter-2.html" class="internal"><span class="codenumber">A</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table</span></a></div>
|
||||
<ul class="structural toc-item-list"><li class="toc-item toc-section"><div class="toc-title-box"><a href="app-Phi-table.html" class="internal"><span class="codenumber">A.1</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table of Values</span></a></div></li></ul>
|
||||
</li>
|
||||
<li class="toc-item toc-colophon"><div class="toc-title-box"><a href="backmatter-3.html" class="internal"><span class="title">Colophon</span></a></div></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul></nav></div>
|
||||
<main class="ptx-main"><div id="ptx-content" class="ptx-content"><section class="section" id="sec-Variance"><h2 class="heading hide-type">
|
||||
<span class="type">Section</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">3.2</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Variance</span>
|
||||
|
||||
Reference in New Issue
Block a user