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2026-01-11 13:24:27 -05:00
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@@ -9,7 +9,7 @@
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@@ -101,15 +101,15 @@ eBookConfig.allow_pairs = false;
eBookConfig.enableScratchAC = false;
eBookConfig.build_info = "";
eBookConfig.python3 = null;
eBookConfig.runestone_version = '7.11.5';
eBookConfig.runestone_version = '7.11.8';
eBookConfig.jobehost = '';
eBookConfig.proxyuri_runs = '';
eBookConfig.proxyuri_files = '';
eBookConfig.enable_chatcodes = false;
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@@ -129,7 +129,13 @@ eBookConfig.enable_chatcodes = false;
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</div></nav><div id="latex-macros" class="hidden-content process-math" style="display:none"><span class="process-math">\(\newcommand{\N}{\mathbb N}
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@@ -144,6 +150,7 @@ eBookConfig.enable_chatcodes = false;
\DeclareMathOperator{\E}{E}
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\DeclareMathOperator{\Cov}{Cov}
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@@ -151,9 +158,13 @@ eBookConfig.enable_chatcodes = false;
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\)</span></div>
<div class="ptx-page">
<div id="ptx-sidebar" class="ptx-sidebar"><nav id="ptx-toc" class="ptx-toc depth2 focused" data-preexpanded-levels="0" data-max-levels="2"><ul class="structural toc-item-list contains-active">
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<li class="toc-item toc-frontmatter"><div class="toc-title-box"><a href="frontmatter.html" class="internal"><span class="title">Front Matter</span></a></div></li>
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<div class="toc-title-box"><a href="ch-Introduction.html" class="internal"><span class="codenumber">0</span> <span class="title">Introduction</span></a></div>
<ul class="structural toc-item-list"><li class="toc-item toc-section"><div class="toc-title-box"><a href="sec-Introduction.html" class="internal"><span class="codenumber">0.1</span> <span class="title">Introduction</span></a></div></li></ul>
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<div class="toc-title-box"><a href="ch-Probability.html" class="internal"><span class="codenumber">1</span> <span class="title">Probability Theory</span></a></div>
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@@ -201,6 +212,10 @@ eBookConfig.enable_chatcodes = false;
<li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Continuous-RVs.html#exercises-Continuous-RVs" class="internal"><span class="codenumber">2.2.5</span> <span class="title">Exercises</span></a></div></li>
</ul>
</li>
<li class="toc-item toc-section">
<div class="toc-title-box"><a href="sec-Joint-Distributions.html" class="internal"><span class="codenumber">2.3</span> <span class="title">Joint Distributions</span></a></div>
<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Joint-Distributions.html#exercises-Joint-Distributions" class="internal"><span class="codenumber">2.3</span> <span class="title">Exercises</span></a></div></li></ul>
</li>
</ul>
</li>
<li class="toc-item toc-chapter">
@@ -228,24 +243,48 @@ eBookConfig.enable_chatcodes = false;
<li class="toc-item toc-chapter contains-active">
<div class="toc-title-box"><a href="ch-Confidence-Intervals.html" class="internal"><span class="codenumber">4</span> <span class="title">Confidence Intervals</span></a></div>
<ul class="structural toc-item-list contains-active">
<li class="toc-item toc-section active"><div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Central Limit Theorem</span></a></div></li>
<li class="toc-item toc-section"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Confidence Intervals</span></a></div></li>
<li class="toc-item toc-section contains-active">
<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Central Limit Theorem</span></a></div>
<ul class="structural toc-item-list active"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
</li>
<li class="toc-item toc-section">
<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Confidence Intervals</span></a></div>
<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
</li>
</ul>
</li>
<li class="toc-item toc-chapter">
<div class="toc-title-box"><a href="ch-Hypothesis-Testing.html" class="internal"><span class="codenumber">5</span> <span class="title">Hypothesis Testing</span></a></div>
<ul class="structural toc-item-list">
<li class="toc-item toc-section"><div class="toc-title-box"><a href="sec-One-Sample-Tests.html" class="internal"><span class="codenumber">5.1</span> <span class="title">One Sample Tests</span></a></div></li>
<li class="toc-item toc-section"><div class="toc-title-box"><a href="sec-Two-Sample-Tests.html" class="internal"><span class="codenumber">5.2</span> <span class="title">Two Sample Tests</span></a></div></li>
<li class="toc-item toc-section"><div class="toc-title-box"><a href="sec-Power.html" class="internal"><span class="codenumber">5.3</span> <span class="title">Power of a Test</span></a></div></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></li>
<li class="toc-item toc-section">
<div class="toc-title-box"><a href="sec-One-Sample-Tests.html" class="internal"><span class="codenumber">5.1</span> <span class="title">One Sample Tests</span></a></div>
<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-One-Sample-Tests.html#exercises-One-Sample-Tests" class="internal"><span class="codenumber">5.1</span> <span class="title">Exercises</span></a></div></li></ul>
</li>
<li class="toc-item toc-section">
<div class="toc-title-box"><a href="sec-Two-Sample-Tests.html" class="internal"><span class="codenumber">5.2</span> <span class="title">Two Sample Tests</span></a></div>
<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Two-Sample-Tests.html#exercises-Two-Sample-Tests" class="internal"><span class="codenumber">5.2</span> <span class="title">Exercises</span></a></div></li></ul>
</li>
<li class="toc-item toc-section">
<div class="toc-title-box"><a href="sec-Power.html" class="internal"><span class="codenumber">5.3</span> <span class="title">Power of a Test</span></a></div>
<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Power.html#exercises-Power" class="internal"><span class="codenumber">5.3</span> <span class="title">Exercises</span></a></div></li></ul>
</li>
<li class="toc-item toc-section">
<div class="toc-title-box"><a href="sec-Chi-Squared.html" class="internal"><span class="codenumber">5.4</span> <span class="title"><span class="process-math">\(\chi^2\)</span> Test</span></a></div>
<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Chi-Squared.html#exercises-Chi-Squared" class="internal"><span class="codenumber">5.4</span> <span class="title">Exercises</span></a></div></li></ul>
</li>
</ul>
</li>
<li class="toc-item toc-chapter">
<div class="toc-title-box"><a href="ch-Linear-Regression.html" class="internal"><span class="codenumber">6</span> <span class="title">Linear Regression</span></a></div>
<ul class="structural toc-item-list">
<li class="toc-item toc-section"><div class="toc-title-box"><a href="sec-Correlation.html" class="internal"><span class="codenumber">6.1</span> <span class="title">Correlation</span></a></div></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></li>
<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>
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</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>
@@ -255,7 +294,28 @@ eBookConfig.enable_chatcodes = false;
</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>
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<div class="autopermalink" data-description="Section 4.1: Central Limit Theorem"><a href="#sec-CLT" title="Copy heading and permalink for Section 4.1: Central Limit Theorem" aria-label="Copy heading and permalink for Section 4.1: Central Limit Theorem">🔗</a></div></section></div>
<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>
</h3>
<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="autopermalink" data-description="Exercise 4.1.1"><a href="#exercises-CLT-1" title="Copy heading and permalink for Exercise 4.1.1" aria-label="Copy heading and permalink for Exercise 4.1.1">🔗</a></div></article><article class="exercise exercise-like" id="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="autopermalink" data-description="Exercise 4.1.2"><a href="#exercises-CLT-2" title="Copy heading and permalink for Exercise 4.1.2" aria-label="Copy heading and permalink for Exercise 4.1.2">🔗</a></div></article><article class="exercise exercise-like" id="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="autopermalink" data-description="Task 4.1.3.a"><a href="#exercises-CLT-3-2" title="Copy heading and permalink for Task 4.1.3.a" aria-label="Copy heading and permalink for Task 4.1.3.a">🔗</a></div></article><article class="task exercise-like" id="exercises-CLT-3-3"><h5 class="heading"><span class="codenumber">(b)</span></h5>
<div class="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 4.1.3.b"><a href="#exercises-CLT-3-3" title="Copy heading and permalink for Task 4.1.3.b" aria-label="Copy heading and permalink for Task 4.1.3.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>
<div class="autopermalink" data-description="Task 4.1.3.c"><a href="#exercises-CLT-3-4" title="Copy heading and permalink for Task 4.1.3.c" aria-label="Copy heading and permalink for Task 4.1.3.c">🔗</a></div></article><div class="autopermalink" data-description="Exercise 4.1.3"><a href="#exercises-CLT-3" title="Copy heading and permalink for Exercise 4.1.3" aria-label="Copy heading and permalink for Exercise 4.1.3">🔗</a></div></article><div class="autopermalink" data-description="Exercises 4.1"><a href="#exercises-CLT" title="Copy heading and permalink for Exercises 4.1" aria-label="Copy heading and permalink for Exercises 4.1">🔗</a></div></section><div class="autopermalink" data-description="Section 4.1: Central Limit Theorem"><a href="#sec-CLT" title="Copy heading and permalink for Section 4.1: Central Limit Theorem" aria-label="Copy heading and permalink for Section 4.1: Central Limit Theorem">🔗</a></div></section></div>
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