Latest build deployed.

course/.mapping.json

@@ -1 +1 @@
-{"source/main.ptx": ["frontmatter", "course-documents", "ch-notes", "quizzes", "exams", "recitations", "review"], "source/syllabus/syllabus.ptx": ["syllabus"], "source/notes/1-13.ptx": ["notes-01-13"], "source/notes/1-15.ptx": ["notes-01-15"], "source/notes/1-20.ptx": ["notes-01-20"], "source/notes/1-22.ptx": ["notes-01-22"], "source/notes/1-27.ptx": ["notes-01-27"], "source/notes/1-29.ptx": ["notes-01-29"], "source/notes/2-3.ptx": ["notes-02-03"], "source/notes/2-5.ptx": ["notes-02-05"], "source/notes/2-10.ptx": ["notes-02-10"], "source/notes/2-19.ptx": ["notes-02-19"], "source/notes/2-24.ptx": ["notes-02-24"], "source/quizzes/quiz-01.ptx": ["quiz-01"], "source/quizzes/quiz-02.ptx": ["quiz-02"], "source/exams/exam-01.ptx": ["exam-01"], "source/recitations/calculus-review.ptx": ["recitation-calculus-review"], "source/review/Exam-1-Review.ptx": ["Exam-1-Review"]}
+{"source/main.ptx": ["frontmatter", "course-documents", "ch-notes", "quizzes", "exams", "recitations", "review"], "source/syllabus/syllabus.ptx": ["syllabus"], "source/notes/1-13.ptx": ["notes-01-13"], "source/notes/1-15.ptx": ["notes-01-15"], "source/notes/1-20.ptx": ["notes-01-20"], "source/notes/1-22.ptx": ["notes-01-22"], "source/notes/1-27.ptx": ["notes-01-27"], "source/notes/1-29.ptx": ["notes-01-29"], "source/notes/2-3.ptx": ["notes-02-03"], "source/notes/2-5.ptx": ["notes-02-05"], "source/notes/2-10.ptx": ["notes-02-10"], "source/notes/2-19.ptx": ["notes-02-19"], "source/notes/2-24.ptx": ["notes-02-24"], "source/quizzes/quiz-01.ptx": ["quiz-01"], "source/quizzes/quiz-02.ptx": ["quiz-02"], "source/quizzes/quiz-03.ptx": ["quiz-03"], "source/exams/exam-01.ptx": ["exam-01"], "source/recitations/calculus-review.ptx": ["recitation-calculus-review"], "source/review/Exam-1-Review.ptx": ["Exam-1-Review"]}

course/Exam-1-Review.html

@@ -250,6 +250,7 @@ eBookConfig.enable_chatcodes =  false;
 <ul class="structural toc-item-list">
 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-01.html" class="internal"><span class="title">Quiz 1</span></a></div></li>
 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-02.html" class="internal"><span class="title">Quiz 2</span></a></div></li>
+<li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-03.html" class="internal"><span class="title">Quiz 3</span></a></div></li>
 </ul>
 </li>
 <li class="toc-item toc-chapter">
@@ -369,7 +370,7 @@ eBookConfig.enable_chatcodes =  false;
 </div></details></div>
 <div class="autopermalink" data-description="Exercise 4"><a href="#Exam-1-Review-4-4" title="Copy heading and permalink for Exercise 4" aria-label="Copy heading and permalink for Exercise 4">🔗</a></div></article><article class="exercise exercise-like" id="Exam-1-Review-4-5"><h4 class="heading"><span class="codenumber">5<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
 <div class="para" id="Exam-1-Review-4-5-1-1">Consider the sample space <span class="process-math">\(\Omega = \{1, 2, 3, 4, 5, 6, 7, 8\}\)</span> with probability distribution below. Calculate the probabilities of <span class="process-math">\(A = \{1, 3, 7, 8\}\text{,}\)</span> <span class="process-math">\(B = \{2, 3, 6, 7\}\text{,}\)</span> <span class="process-math">\(A\cup B\text{,}\)</span> and <span class="process-math">\(A \cap B\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#Exam-1-Review-4-5-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
-</div> <figure class="table table-like" id="Exam-1-Review-4-5-1-2"><figcaption><span class="type">Table</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">127<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span><div class="autopermalink" data-description="Table 127: "><a href="#Exam-1-Review-4-5-1-2" title="Copy heading and permalink for Table 127: " aria-label="Copy heading and permalink for Table 127: ">🔗</a></div></figcaption><div class="tabular-box natural-width"><table class="tabular">
+</div> <figure class="table table-like" id="Exam-1-Review-4-5-1-2"><figcaption><span class="type">Table</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">128<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span><div class="autopermalink" data-description="Table 128: "><a href="#Exam-1-Review-4-5-1-2" title="Copy heading and permalink for Table 128: " aria-label="Copy heading and permalink for Table 128: ">🔗</a></div></figcaption><div class="tabular-box natural-width"><table class="tabular">
 <tr>
 <td class="c m b1 r0 l0 t0 lines"><span class="process-math">\(x\)</span></td>
 <td class="c m b1 r0 l0 t0 lines"><span class="process-math">\(\Pr(x)\)</span></td>
@@ -420,7 +421,7 @@ eBookConfig.enable_chatcodes =  false;
 <div class="para" id="Exam-1-Review-4-6-1-1">Suppose a die has the values <span class="process-math">\(1, 2, 3, 4, 5, 6\)</span> on the faces, but the die is not fair. Instead, the probabilities scale by the same amount as the face values. For example, a result of 4 is twice as likely as a result of 2, since 4 is twice as large as 2; a result of 6 is six times more likely than a result of 1; and so on. Write a probability distribution table for this die.<div class="autopermalink" data-description="Paragraph"><a href="#Exam-1-Review-4-6-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
 </div>
 <div class="solutions"><details id="Exam-1-Review-4-6-2" class="answer solution-like born-hidden-knowl"><summary class="knowl__link"><span class="type">Answer</span><span class="period heading-divison-mark heading-divison-mark__period">.</span></summary><div class="answer solution-like knowl__content">
-<figure class="table table-like" id="Exam-1-Review-4-6-2-1"><figcaption><span class="type">Table</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">128<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span>Probability Distribution for a Linearly Scaled Die<div class="autopermalink" data-description="Table 128: Probability Distribution for a Linearly Scaled Die"><a href="#Exam-1-Review-4-6-2-1" title="Copy heading and permalink for Table 128: Probability Distribution for a Linearly Scaled Die" aria-label="Copy heading and permalink for Table 128: Probability Distribution for a Linearly Scaled Die">🔗</a></div></figcaption><div class="tabular-box natural-width"><table class="tabular">
+<figure class="table table-like" id="Exam-1-Review-4-6-2-1"><figcaption><span class="type">Table</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">129<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span>Probability Distribution for a Linearly Scaled Die<div class="autopermalink" data-description="Table 129: Probability Distribution for a Linearly Scaled Die"><a href="#Exam-1-Review-4-6-2-1" title="Copy heading and permalink for Table 129: Probability Distribution for a Linearly Scaled Die" aria-label="Copy heading and permalink for Table 129: Probability Distribution for a Linearly Scaled Die">🔗</a></div></figcaption><div class="tabular-box natural-width"><table class="tabular">
 <tr>
 <td class="c m b1 r0 l0 t0 lines"><span class="process-math">\(x\)</span></td>
 <td class="c m b1 r0 l0 t0 lines"><span class="process-math">\(\Pr(x)\)</span></td>
@@ -455,7 +456,7 @@ eBookConfig.enable_chatcodes =  false;
 <div class="para" id="Exam-1-Review-4-7-1-1">Suppose a die has the values <span class="process-math">\(1, 2, 3, 4, 5, 6\)</span> on the faces, but the die is not fair. Instead, each even value has an equal probability, each odd value has an equal probability, and the even values are each twice as likely as the odd values to appear on a roll. Write a probability distribution table for this die.<div class="autopermalink" data-description="Paragraph"><a href="#Exam-1-Review-4-7-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
 </div>
 <div class="solutions"><details id="Exam-1-Review-4-7-2" class="answer solution-like born-hidden-knowl"><summary class="knowl__link"><span class="type">Answer</span><span class="period heading-divison-mark heading-divison-mark__period">.</span></summary><div class="answer solution-like knowl__content">
-<figure class="table table-like" id="Exam-1-Review-4-7-2-1"><figcaption><span class="type">Table</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">129<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span>Probability Distribution for an Even-biased Die<div class="autopermalink" data-description="Table 129: Probability Distribution for an Even-biased Die"><a href="#Exam-1-Review-4-7-2-1" title="Copy heading and permalink for Table 129: Probability Distribution for an Even-biased Die" aria-label="Copy heading and permalink for Table 129: Probability Distribution for an Even-biased Die">🔗</a></div></figcaption><div class="tabular-box natural-width"><table class="tabular">
+<figure class="table table-like" id="Exam-1-Review-4-7-2-1"><figcaption><span class="type">Table</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">130<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span>Probability Distribution for an Even-biased Die<div class="autopermalink" data-description="Table 130: Probability Distribution for an Even-biased Die"><a href="#Exam-1-Review-4-7-2-1" title="Copy heading and permalink for Table 130: Probability Distribution for an Even-biased Die" aria-label="Copy heading and permalink for Table 130: Probability Distribution for an Even-biased Die">🔗</a></div></figcaption><div class="tabular-box natural-width"><table class="tabular">
 <tr>
 <td class="c m b1 r0 l0 t0 lines"><span class="process-math">\(x\)</span></td>
 <td class="c m b1 r0 l0 t0 lines"><span class="process-math">\(\Pr(x)\)</span></td>
@@ -649,7 +650,7 @@ A\cap B \amp = \{HHH, HHT\}
 <div class="para" id="Exam-1-Review-4-13-1-1">Let <span class="process-math">\(A = \{1, 2, 3\}\)</span> and <span class="process-math">\(B = \{3, 4, 5\}\)</span> be events in the sample space <span class="process-math">\(\Omega = \{1, 2, 3, 4, 5, 6\}\text{.}\)</span> Create a probability distribution for <span class="process-math">\(\Omega\)</span> so that <span class="process-math">\(A, B\)</span> are independent.<div class="autopermalink" data-description="Paragraph"><a href="#Exam-1-Review-4-13-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
 </div>
 <div class="solutions"><details id="Exam-1-Review-4-13-2" class="answer solution-like born-hidden-knowl"><summary class="knowl__link"><span class="type">Answer</span><span class="period heading-divison-mark heading-divison-mark__period">.</span></summary><div class="answer solution-like knowl__content">
-<figure class="table table-like" id="Exam-1-Review-4-13-2-1"><figcaption><span class="type">Table</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">130<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span>Example Distribution<div class="autopermalink" data-description="Table 130: Example Distribution"><a href="#Exam-1-Review-4-13-2-1" title="Copy heading and permalink for Table 130: Example Distribution" aria-label="Copy heading and permalink for Table 130: Example Distribution">🔗</a></div></figcaption><div class="tabular-box natural-width"><table class="tabular">
+<figure class="table table-like" id="Exam-1-Review-4-13-2-1"><figcaption><span class="type">Table</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">131<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span>Example Distribution<div class="autopermalink" data-description="Table 131: Example Distribution"><a href="#Exam-1-Review-4-13-2-1" title="Copy heading and permalink for Table 131: Example Distribution" aria-label="Copy heading and permalink for Table 131: Example Distribution">🔗</a></div></figcaption><div class="tabular-box natural-width"><table class="tabular">
 <tr>
 <td class="c m b1 r0 l0 t0 lines"><span class="process-math">\(x\)</span></td>
 <td class="c m b1 r0 l0 t0 lines"><span class="process-math">\(\Pr(x)\)</span></td>
@@ -774,7 +775,7 @@ A\cap B \amp = \{HHH, HHT\}
 </div></details></div>
 <div class="autopermalink" data-description="Exercise 20"><a href="#Exam-1-Review-4-19" title="Copy heading and permalink for Exercise 20" aria-label="Copy heading and permalink for Exercise 20">🔗</a></div></article><article class="exercise exercise-like" id="Exam-1-Review-4-20"><h4 class="heading"><span class="codenumber">21<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
 <div class="para" id="Exam-1-Review-4-20-1-1">Consider <span class="process-math">\(X, Y\)</span> with the joint distribution table below. Are <span class="process-math">\(X, Y\)</span> independent?<div class="autopermalink" data-description="Paragraph"><a href="#Exam-1-Review-4-20-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
-</div> <figure class="table table-like" id="Exam-1-Review-4-20-1-2"><figcaption><span class="type">Table</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">131<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span>Joint distribution for <span class="process-math">\(X, Y\)</span><div class="autopermalink" data-description="Table 131: Joint distribution for X, Y"><a href="#Exam-1-Review-4-20-1-2" title="Copy heading and permalink for Table 131: Joint distribution for X, Y" aria-label="Copy heading and permalink for Table 131: Joint distribution for X, Y">🔗</a></div></figcaption><div class="tabular-box natural-width"><table class="tabular">
+</div> <figure class="table table-like" id="Exam-1-Review-4-20-1-2"><figcaption><span class="type">Table</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">132<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span>Joint distribution for <span class="process-math">\(X, Y\)</span><div class="autopermalink" data-description="Table 132: Joint distribution for X, Y"><a href="#Exam-1-Review-4-20-1-2" title="Copy heading and permalink for Table 132: Joint distribution for X, Y" aria-label="Copy heading and permalink for Table 132: Joint distribution for X, Y">🔗</a></div></figcaption><div class="tabular-box natural-width"><table class="tabular">
 <tr>
 <td class="c m b1 r1 l0 t0 lines"></td>
 <td class="c m b1 r1 l0 t0 lines"><span class="process-math">\(X = 0\)</span></td>
@@ -809,7 +810,7 @@ A\cap B \amp = \{HHH, HHT\}
 <div class="autopermalink" data-description="Paragraph"><a href="#Exam-1-Review-4-21-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
 </div>
 <div class="solutions"><details id="Exam-1-Review-4-21-2" class="answer solution-like born-hidden-knowl"><summary class="knowl__link"><span class="type">Answer</span><span class="period heading-divison-mark heading-divison-mark__period">.</span></summary><div class="answer solution-like knowl__content">
-<figure class="table table-like" id="Exam-1-Review-4-21-2-1"><figcaption><span class="type">Table</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">132<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span>Joint Distribution<div class="autopermalink" data-description="Table 132: Joint Distribution"><a href="#Exam-1-Review-4-21-2-1" title="Copy heading and permalink for Table 132: Joint Distribution" aria-label="Copy heading and permalink for Table 132: Joint Distribution">🔗</a></div></figcaption><div class="tabular-box natural-width"><table class="tabular">
+<figure class="table table-like" id="Exam-1-Review-4-21-2-1"><figcaption><span class="type">Table</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">133<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span>Joint Distribution<div class="autopermalink" data-description="Table 133: Joint Distribution"><a href="#Exam-1-Review-4-21-2-1" title="Copy heading and permalink for Table 133: Joint Distribution" aria-label="Copy heading and permalink for Table 133: Joint Distribution">🔗</a></div></figcaption><div class="tabular-box natural-width"><table class="tabular">
 <tr>
 <td class="c m b1 r1 l0 t0 lines"></td>
 <td class="c m b1 r1 l0 t0 lines"><span class="process-math">\(X = 0\)</span></td>
@@ -832,7 +833,7 @@ A\cap B \amp = \{HHH, HHT\}
 </div></details></div>
 <div class="autopermalink" data-description="Exercise 22"><a href="#Exam-1-Review-4-21" title="Copy heading and permalink for Exercise 22" aria-label="Copy heading and permalink for Exercise 22">🔗</a></div></article><article class="exercise exercise-like" id="Exam-1-Review-4-22"><h4 class="heading"><span class="codenumber">23<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
 <div class="para" id="Exam-1-Review-4-22-1-1">Consider a random variable <span class="process-math">\(X\)</span> with probability distribution below. Find <span class="process-math">\(\E(X)\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#Exam-1-Review-4-22-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
-</div> <figure class="table table-like" id="Exam-1-Review-4-22-1-2"><figcaption><span class="type">Table</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">133<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span><div class="autopermalink" data-description="Table 133: "><a href="#Exam-1-Review-4-22-1-2" title="Copy heading and permalink for Table 133: " aria-label="Copy heading and permalink for Table 133: ">🔗</a></div></figcaption><div class="tabular-box natural-width"><table class="tabular">
+</div> <figure class="table table-like" id="Exam-1-Review-4-22-1-2"><figcaption><span class="type">Table</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">134<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span><div class="autopermalink" data-description="Table 134: "><a href="#Exam-1-Review-4-22-1-2" title="Copy heading and permalink for Table 134: " aria-label="Copy heading and permalink for Table 134: ">🔗</a></div></figcaption><div class="tabular-box natural-width"><table class="tabular">
 <tr class="header-horizontal">
 <th scope="col" class="c m b1 r0 l0 t0 lines"><span class="process-math">\(x\)</span></th>
 <th scope="col" class="c m b1 r0 l0 t0 lines"><span class="process-math">\(\Pr(X = x)\)</span></th>
@@ -941,7 +942,7 @@ A\cap B \amp = \{HHH, HHT\}
 </div></details></div>
 <div class="autopermalink" data-description="Exercise 28"><a href="#Exam-1-Review-4-27" title="Copy heading and permalink for Exercise 28" aria-label="Copy heading and permalink for Exercise 28">🔗</a></div></article><article class="exercise exercise-like" id="Exam-1-Review-4-28"><h4 class="heading"><span class="codenumber">29<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
 <div class="para" id="Exam-1-Review-4-28-1-1">Consider a random variable <span class="process-math">\(X\)</span> with probability distribution below. Find <span class="process-math">\(\Var(X)\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#Exam-1-Review-4-28-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
-</div> <figure class="table table-like" id="Exam-1-Review-4-28-1-2"><figcaption><span class="type">Table</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">134<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span><div class="autopermalink" data-description="Table 134: "><a href="#Exam-1-Review-4-28-1-2" title="Copy heading and permalink for Table 134: " aria-label="Copy heading and permalink for Table 134: ">🔗</a></div></figcaption><div class="tabular-box natural-width"><table class="tabular">
+</div> <figure class="table table-like" id="Exam-1-Review-4-28-1-2"><figcaption><span class="type">Table</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">135<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span><div class="autopermalink" data-description="Table 135: "><a href="#Exam-1-Review-4-28-1-2" title="Copy heading and permalink for Table 135: " aria-label="Copy heading and permalink for Table 135: ">🔗</a></div></figcaption><div class="tabular-box natural-width"><table class="tabular">
 <tr class="header-horizontal">
 <th scope="col" class="c m b1 r0 l0 t0 lines"><span class="process-math">\(x\)</span></th>
 <th scope="col" class="c m b1 r0 l0 t0 lines"><span class="process-math">\(\Pr(X = x)\)</span></th>

course/ch-notes.html

@@ -250,6 +250,7 @@ eBookConfig.enable_chatcodes =  false;
 <ul class="structural toc-item-list">
 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-01.html" class="internal"><span class="title">Quiz 1</span></a></div></li>
 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-02.html" class="internal"><span class="title">Quiz 2</span></a></div></li>
+<li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-03.html" class="internal"><span class="title">Quiz 3</span></a></div></li>
 </ul>
 </li>
 <li class="toc-item toc-chapter">

course/course-documents.html

@@ -250,6 +250,7 @@ eBookConfig.enable_chatcodes =  false;
 <ul class="structural toc-item-list">
 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-01.html" class="internal"><span class="title">Quiz 1</span></a></div></li>
 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-02.html" class="internal"><span class="title">Quiz 2</span></a></div></li>
+<li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-03.html" class="internal"><span class="title">Quiz 3</span></a></div></li>
 </ul>
 </li>
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course/exam-01.html

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course/exams.html

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course/frontmatter.html

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course/index.html

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course/lunr-pretext-search-index.js

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   "body": "  Suppose a continuous random variable taking values in has cdf .     Find the pdf .           Find .         "
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+{
+  "id": "quiz-03",
+  "level": "1",
+  "url": "quiz-03.html",
+  "type": "Worksheet",
+  "number": "",
+  "title": "Quiz 3",
+  "body": " Quiz 3    The following work should be completed individually. Use of notes or textbooks is not allowed. You may use a scientific calculator, not a graphing calculator or phone app.  Show all work unless instructed otherwise.       Write either True or False for each of the following statements. No justification is required.     Suppose a parameter has likelihood function with . Then the maximum likelihood estimation is .    True.      Suppose are random variables, and . Then, for sufficiently large , .    False.      Suppose we collect data to estimate the value of a parameter . Based on the collected data, we find a 95% confidence interval and a 90% confidence interval . Then .    True.       The heights of five plants are measured and recorded below. Find the sample mean, sample variance, and a 95% confidence interval around the sample mean for the heights of the plants. (Pretend that 5 measurements is enough for the CLT to apply.)    Plant  (in)                          Let be the average height of the sample. Then: So the 95% confidence limits are:         Suppose a coin comes up heads with probability 0.6. We flip the coin 80 times, and let be the number of heads. Estimate . (Use a continuity correction if appropriate.)     , so and . By the CLT, , so:      Values     0.00  0.01  0.02  0.03  0.04  0.05  0.06  0.07  0.08  0.09    −1.6  0.0548  0.0537  0.0526  0.0516  0.0505  0.0495  0.0485  0.0475  0.0465  0.0455    −1.5  0.0668  0.0655  0.0643  0.0630  0.0618  0.0606  0.0594  0.0582  0.0571  0.0559    −1.4  0.0808  0.0793  0.0778  0.0764  0.0749  0.0735  0.0721  0.0708  0.0694  0.0681    −1.3  0.0968  0.0951  0.0934  0.0918  0.0901  0.0885  0.0869  0.0853  0.0838  0.0823    −1.2  0.1151  0.1131  0.1112  0.1093  0.1075  0.1056  0.1038  0.1020  0.1003  0.0985    0.2  0.5793  0.5832  0.5871  0.5910  0.5948  0.5987  0.6026  0.6064  0.6103  0.6141    0.3  0.6179  0.6217  0.6255  0.6293  0.6331  0.6368  0.6406  0.6443  0.6480  0.6517    0.4  0.6554  0.6591  0.6628  0.6664  0.6700  0.6736  0.6772  0.6808  0.6844  0.6879    0.5  0.6915  0.6950  0.6985  0.7019  0.7054  0.7088  0.7123  0.7157  0.7190  0.7224    0.6  0.7257  0.7291  0.7324  0.7357  0.7389  0.7422  0.7454  0.7486  0.7517  0.7549      "
+},
+{
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+  "level": "2",
+  "url": "quiz-03.html#quiz-03-3-1",
+  "type": "Worksheet Exercise",
+  "number": "1",
+  "title": "",
+  "body": "  Write either True or False for each of the following statements. No justification is required.     Suppose a parameter has likelihood function with . Then the maximum likelihood estimation is .    True.      Suppose are random variables, and . Then, for sufficiently large , .    False.      Suppose we collect data to estimate the value of a parameter . Based on the collected data, we find a 95% confidence interval and a 90% confidence interval . Then .    True.    "
+},
+{
+  "id": "quiz-03-3-2",
+  "level": "2",
+  "url": "quiz-03.html#quiz-03-3-2",
+  "type": "Worksheet Exercise",
+  "number": "2",
+  "title": "",
+  "body": "  The heights of five plants are measured and recorded below. Find the sample mean, sample variance, and a 95% confidence interval around the sample mean for the heights of the plants. (Pretend that 5 measurements is enough for the CLT to apply.)    Plant  (in)                          Let be the average height of the sample. Then: So the 95% confidence limits are:    "
+},
+{
+  "id": "quiz-03-4-1",
+  "level": "2",
+  "url": "quiz-03.html#quiz-03-4-1",
+  "type": "Worksheet Exercise",
+  "number": "3",
+  "title": "",
+  "body": "  Suppose a coin comes up heads with probability 0.6. We flip the coin 80 times, and let be the number of heads. Estimate . (Use a continuity correction if appropriate.)     , so and . By the CLT, , so:    "
+},
+{
+  "id": "quiz-03-4-2",
+  "level": "2",
+  "url": "quiz-03.html#quiz-03-4-2",
+  "type": "Table",
+  "number": "126",
+  "title": "<span class=\"process-math\">\\(\\Phi(z)\\)<\/span> Values",
+  "body": " Values     0.00  0.01  0.02  0.03  0.04  0.05  0.06  0.07  0.08  0.09    −1.6  0.0548  0.0537  0.0526  0.0516  0.0505  0.0495  0.0485  0.0475  0.0465  0.0455    −1.5  0.0668  0.0655  0.0643  0.0630  0.0618  0.0606  0.0594  0.0582  0.0571  0.0559    −1.4  0.0808  0.0793  0.0778  0.0764  0.0749  0.0735  0.0721  0.0708  0.0694  0.0681    −1.3  0.0968  0.0951  0.0934  0.0918  0.0901  0.0885  0.0869  0.0853  0.0838  0.0823    −1.2  0.1151  0.1131  0.1112  0.1093  0.1075  0.1056  0.1038  0.1020  0.1003  0.0985    0.2  0.5793  0.5832  0.5871  0.5910  0.5948  0.5987  0.6026  0.6064  0.6103  0.6141    0.3  0.6179  0.6217  0.6255  0.6293  0.6331  0.6368  0.6406  0.6443  0.6480  0.6517    0.4  0.6554  0.6591  0.6628  0.6664  0.6700  0.6736  0.6772  0.6808  0.6844  0.6879    0.5  0.6915  0.6950  0.6985  0.7019  0.7054  0.7088  0.7123  0.7157  0.7190  0.7224    0.6  0.7257  0.7291  0.7324  0.7357  0.7389  0.7422  0.7454  0.7486  0.7517  0.7549    "
+},
 {
   "id": "exam-01",
   "level": "1",
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   "level": "2",
   "url": "recitation-calculus-review.html#thm-FTC",
   "type": "Theorem",
-  "number": "126",
+  "number": "127",
   "title": "Fundamental Theorem of Calculus.",
   "body": " Fundamental Theorem of Calculus   If is an antiderivative of i.e., if then:    "
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course/notes-01-13.html

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course/notes-01-15.html

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course/notes-01-20.html

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course/notes-01-22.html

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course/notes-01-27.html

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course/notes-01-29.html

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course/notes-02-03.html

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course/notes-02-05.html

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course/notes-02-10.html

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course/notes-02-19.html

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course/notes-02-24.html

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course/quiz-01.html

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course/quiz-02.html

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+<p class="byline">Andy Eisenberg</p>
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+<div class="toc-title-box"><a href="ch-notes.html" class="internal"><span class="title">Class Notes</span></a></div>
+<ul class="structural toc-item-list">
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="notes-01-13.html" class="internal"><span class="title">Tuesday, Jan 13</span></a></div>
+<ul class="structural toc-item-list">
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-01-13.html#subsec-Sets" class="internal"><span class="title">Sec 1.1: Sets</span></a></div></li>
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-01-13.html#subsec-Probability" class="internal"><span class="title">Sec 1.2: Probability</span></a></div></li>
+</ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="notes-01-15.html" class="internal"><span class="title">Thursday, Jan 15</span></a></div>
+<ul class="structural toc-item-list">
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-01-15.html#subsec-Conditional-Probability" class="internal"><span class="title">Sec 1.3: Conditional Probability</span></a></div></li>
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+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-01-15.html#subsec-Independent-Events" class="internal"><span class="title">Sec 1.4: Independent Events</span></a></div></li>
+</ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="notes-01-20.html" class="internal"><span class="title">Tuesday, Jan 20</span></a></div>
+<ul class="structural toc-item-list">
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-01-20.html#subsec-hw1-review" class="internal"><span class="title">HW 1 Q5</span></a></div></li>
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-01-20.html#subsec-Discrete-Random-Variables" class="internal"><span class="title">Sec 2.1: Random Variables</span></a></div></li>
+</ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="notes-01-22.html" class="internal"><span class="title">Thursday, Jan 22</span></a></div>
+<ul class="structural toc-item-list">
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-01-22.html#subsec-discrete-distributions" class="internal"><span class="title">Discrete Distributions</span></a></div></li>
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-01-22.html#subsec-continuous-distributions" class="internal"><span class="title">Continuous Distributions</span></a></div></li>
+</ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="notes-01-27.html" class="internal"><span class="title">Tuesday, Jan 27</span></a></div>
+<ul class="structural toc-item-list">
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-01-27.html#subsec-continuous-2" class="internal"><span class="title">Continuous Distributions</span></a></div></li>
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-01-27.html#subsec-Joint-Distributions" class="internal"><span class="title">Joint Distributions</span></a></div></li>
+</ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="notes-01-29.html" class="internal"><span class="title">Thursday, Jan 29</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-01-29.html#notes-01-29-3" class="internal"><span class="title">Expected Value</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="notes-02-03.html" class="internal"><span class="title">Tuesday, Feb 3</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-02-03.html#notes-02-03-3" class="internal"><span class="title">Variance</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="notes-02-05.html" class="internal"><span class="title">Thursday, Feb 5</span></a></div>
+<ul class="structural toc-item-list">
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-02-05.html#notes-02-05-3" class="internal"><span class="title">Summary</span></a></div></li>
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-02-05.html#notes-02-05-4" class="internal"><span class="title">Covariance</span></a></div></li>
+</ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="notes-02-10.html" class="internal"><span class="title">Tuesday, Feb 10</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-02-10.html#notes-02-10-3" class="internal"><span class="title">Likelihood</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="notes-02-19.html" class="internal"><span class="title">Thursday, Feb 19</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-02-19.html#notes-02-19-3" class="internal"><span class="title">Central Limit Theorem</span></a></div></li></ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="notes-02-24.html" class="internal"><span class="title">Tuesday, Feb 24</span></a></div>
+<ul class="structural toc-item-list">
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-02-24.html#notes-02-24-3" class="internal"><span class="title">More Central Limit Theorem</span></a></div></li>
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-02-24.html#notes-02-24-4" class="internal"><span class="title">Confidence Intervals</span></a></div></li>
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+<button class="print-button" title="Print" onClick="window.print()"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe8ad;</span><span class="name">Print</span></button>
+</div>
+</div>
+<section class="worksheet" id="quiz-03" data-margins="0.5in 0.5in 0.5in 0.5in"><h2 class="heading hide-type">
+<span class="type">Worksheet</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">Quiz 3</span><div class="print-links"><a href="?printpreview=quiz-03" class="print-link" title="Print preview"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe8ad;</span></a></div>
+</h2>
+<section class="introduction" id="quiz-03-2"><div class="para" id="quiz-03-2-1">The following work should be completed individually. Use of notes or textbooks is not allowed. You may use a scientific calculator, not a graphing calculator or phone app.<div class="autopermalink" data-description="Paragraph"><a href="#quiz-03-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="para" id="quiz-03-2-2">Show all work unless instructed otherwise.<div class="autopermalink" data-description="Paragraph"><a href="#quiz-03-2-2" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div></section><section class="onepage" id="quiz-03-3"><article class="exercise exercise-like" id="quiz-03-3-1"><h3 class="heading"><span class="codenumber">1<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h3>
+<div class="introduction" id="quiz-03-3-1-1"><div class="para" id="quiz-03-3-1-1-1">Write either True or False for each of the following statements. No justification is required.<div class="autopermalink" data-description="Paragraph"><a href="#quiz-03-3-1-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div></div>
+<article class="task exercise-like" id="quiz-03-3-1-2"><h4 class="heading"><span class="codenumber">(a)</span></h4>
+<div class="para" id="quiz-03-3-1-2-1-1">Suppose a parameter <span class="process-math">\(\theta \in (-\infty, \infty)\)</span> has likelihood function <span class="process-math">\(\mathcal{L}(\theta)\)</span> with <span class="process-math">\(\L'(\theta) = (1 - \theta)e^{\theta}\text{.}\)</span> Then the maximum likelihood estimation is <span class="process-math">\(\widehat{\theta} = 1\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#quiz-03-3-1-2-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="solutions"><details id="quiz-03-3-1-2-2" class="solution solution-like born-hidden-knowl"><summary class="knowl__link"><span class="type">Solution</span><span class="period heading-divison-mark heading-divison-mark__period">.</span></summary><div class="solution solution-like knowl__content">
+<div class="para" id="quiz-03-3-1-2-2-1">True.<div class="autopermalink" data-description="Paragraph"><a href="#quiz-03-3-1-2-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Solution 1.a.1"><a href="#quiz-03-3-1-2-2" title="Copy heading and permalink for Solution 1.a.1" aria-label="Copy heading and permalink for Solution 1.a.1">🔗</a></div>
+</div></details></div>
+<div class="autopermalink" data-description="Task 1.a"><a href="#quiz-03-3-1-2" title="Copy heading and permalink for Task 1.a" aria-label="Copy heading and permalink for Task 1.a">🔗</a></div></article><article class="task exercise-like" id="quiz-03-3-1-3"><h4 class="heading"><span class="codenumber">(b)</span></h4>
+<div class="para" id="quiz-03-3-1-3-1-1">Suppose <span class="process-math">\(X_1, \dotsc, X_n\)</span> are random variables, and <span class="process-math">\(S = X_1 + \dotsb + X_n\text{.}\)</span> Then, for sufficiently large <span class="process-math">\(n\text{,}\)</span> <span class="process-math">\(S \approx \operatorname{N}(0, 1)\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#quiz-03-3-1-3-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="solutions"><details id="quiz-03-3-1-3-2" class="solution solution-like born-hidden-knowl"><summary class="knowl__link"><span class="type">Solution</span><span class="period heading-divison-mark heading-divison-mark__period">.</span></summary><div class="solution solution-like knowl__content">
+<div class="para" id="quiz-03-3-1-3-2-1">False.<div class="autopermalink" data-description="Paragraph"><a href="#quiz-03-3-1-3-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Solution 1.b.1"><a href="#quiz-03-3-1-3-2" title="Copy heading and permalink for Solution 1.b.1" aria-label="Copy heading and permalink for Solution 1.b.1">🔗</a></div>
+</div></details></div>
+<div class="autopermalink" data-description="Task 1.b"><a href="#quiz-03-3-1-3" title="Copy heading and permalink for Task 1.b" aria-label="Copy heading and permalink for Task 1.b">🔗</a></div></article><article class="task exercise-like" id="quiz-03-3-1-4"><h4 class="heading"><span class="codenumber">(c)</span></h4>
+<div class="para" id="quiz-03-3-1-4-1-1">Suppose we collect data to estimate the value of a parameter <span class="process-math">\(\theta\text{.}\)</span> Based on the collected data, we find a 95% confidence interval <span class="process-math">\([a, b]\)</span> and a 90% confidence interval <span class="process-math">\([c, d]\text{.}\)</span> Then <span class="process-math">\(a \leq c \leq d \leq b\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#quiz-03-3-1-4-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="solutions"><details id="quiz-03-3-1-4-2" class="solution solution-like born-hidden-knowl"><summary class="knowl__link"><span class="type">Solution</span><span class="period heading-divison-mark heading-divison-mark__period">.</span></summary><div class="solution solution-like knowl__content">
+<div class="para" id="quiz-03-3-1-4-2-1">True.<div class="autopermalink" data-description="Paragraph"><a href="#quiz-03-3-1-4-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Solution 1.c.1"><a href="#quiz-03-3-1-4-2" title="Copy heading and permalink for Solution 1.c.1" aria-label="Copy heading and permalink for Solution 1.c.1">🔗</a></div>
+</div></details></div>
+<div class="autopermalink" data-description="Task 1.c"><a href="#quiz-03-3-1-4" title="Copy heading and permalink for Task 1.c" aria-label="Copy heading and permalink for Task 1.c">🔗</a></div></article><div class="autopermalink" data-description="Worksheet Exercise 1"><a href="#quiz-03-3-1" title="Copy heading and permalink for Worksheet Exercise 1" aria-label="Copy heading and permalink for Worksheet Exercise 1">🔗</a></div></article><article class="exercise exercise-like" id="quiz-03-3-2"><h3 class="heading"><span class="codenumber">2<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h3>
+<div class="para" id="quiz-03-3-2-1-1">The heights of five plants are measured and recorded below. Find the sample mean, sample variance, and a 95% confidence interval around the sample mean for the heights of the plants. (Pretend that 5 measurements is enough for the CLT to apply.)<div class="autopermalink" data-description="Paragraph"><a href="#quiz-03-3-2-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div> <div class="tabular-box natural-width"><table class="tabular">
+<tr class="header-horizontal">
+<th scope="col" class="c m b1 r0 l0 t0 lines">Plant <span class="process-math">\(i\)</span>
+</th>
+<th scope="col" class="c m b1 r0 l0 t0 lines">
+<span class="process-math">\(H_i\)</span> (in)</th>
+</tr>
+<tr>
+<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(1\)</span></td>
+<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(13\)</span></td>
+</tr>
+<tr>
+<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(2\)</span></td>
+<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(14\)</span></td>
+</tr>
+<tr>
+<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(3\)</span></td>
+<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(10\)</span></td>
+</tr>
+<tr>
+<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(4\)</span></td>
+<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(15\)</span></td>
+</tr>
+<tr>
+<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(5\)</span></td>
+<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(17\)</span></td>
+</tr>
+</table></div>
+<div class="solutions"><details id="quiz-03-3-2-2" class="solution solution-like born-hidden-knowl"><summary class="knowl__link"><span class="type">Solution</span><span class="period heading-divison-mark heading-divison-mark__period">.</span></summary><div class="solution solution-like knowl__content">
+<div class="para logical" id="quiz-03-3-2-2-1">
+<div class="para">Let <span class="process-math">\(A = \frac{H_1 + \dotsb + H_5}{5}\)</span> be the average height of the sample. Then:</div>
+<div class="displaymath process-math" id="quiz-03-3-2-2-1-2">
+\begin{align*}
+A \amp = 13.8 \amp s^2 \amp = \frac{\sum H_i^2 - n(A^2)}{n - 1} = \frac{979 - 5(13.8^2)}{4} = 6.7 \\
+\sum H_i^2 \amp = 979 \amp \sqrt{\frac{s^2}{n}} \amp = \sqrt{\frac{6.7}{5}} \approx 1.16 
+\end{align*}
+</div>
+<div class="para">So the 95% confidence limits are:</div>
+<div class="displaymath process-math" id="quiz-03-3-2-2-1-3">
+\begin{align*}
+\mu_{\ell} \amp = 13.8 - 1.96(1.16) \approx \boxed{11.53} \\
+\mu_{h} \amp = 13.8 + 1.96(1.16) \approx \boxed{16.07} 
+\end{align*}
+</div>
+<div class="autopermalink" data-description="Paragraph"><a href="#quiz-03-3-2-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Solution 2.1"><a href="#quiz-03-3-2-2" title="Copy heading and permalink for Solution 2.1" aria-label="Copy heading and permalink for Solution 2.1">🔗</a></div>
+</div></details></div>
+<div class="autopermalink" data-description="Worksheet Exercise 2"><a href="#quiz-03-3-2" title="Copy heading and permalink for Worksheet Exercise 2" aria-label="Copy heading and permalink for Worksheet Exercise 2">🔗</a></div></article></section><section class="onepage" id="quiz-03-4"><article class="exercise exercise-like" id="quiz-03-4-1"><h3 class="heading"><span class="codenumber">3<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h3>
+<div class="para" id="quiz-03-4-1-1-1">Suppose a coin comes up heads with probability 0.6. We flip the coin 80 times, and let <span class="process-math">\(S\)</span> be the number of heads. Estimate <span class="process-math">\(\Pr(42 \leq S \leq 50)\text{.}\)</span> (Use a continuity correction if appropriate.)<div class="autopermalink" data-description="Paragraph"><a href="#quiz-03-4-1-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="solutions"><details id="quiz-03-4-1-2" class="solution solution-like born-hidden-knowl"><summary class="knowl__link"><span class="type">Solution</span><span class="period heading-divison-mark heading-divison-mark__period">.</span></summary><div class="solution solution-like knowl__content">
+<div class="para logical" id="quiz-03-4-1-2-1">
+<div class="para">
+<span class="process-math">\(S \sim \Bin(80, 0.6)\text{,}\)</span> so <span class="process-math">\(\E(S) = (80)(0.6) = 48\)</span> and <span class="process-math">\(\Var(S) = (80)(0.6)(0.4) = 19.2\text{.}\)</span> By the CLT, <span class="process-math">\(S \approx \Norm(48, 19.2)\text{,}\)</span> so:</div>
+<div class="displaymath process-math" id="quiz-03-4-1-2-1-5">
+\begin{align*}
+\Pr(42 \leq S \leq 50) \amp \approx \Pr\left( \frac{41.5 - 48}{\sqrt{19.2}} \leq Z \leq \frac{50.5 - 48}{\sqrt{19.2}}\right) \\
+\amp \approx \Pr(-1.48 \leq Z \leq 0.57) \\
+\amp = \Phi(0.57) - \Phi(-1.48) \\
+\amp \approx 0.7157 - 0.0694 \\
+\amp = \boxed{0.6463} 
+\end{align*}
+</div>
+<div class="autopermalink" data-description="Paragraph"><a href="#quiz-03-4-1-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Solution 3.1"><a href="#quiz-03-4-1-2" title="Copy heading and permalink for Solution 3.1" aria-label="Copy heading and permalink for Solution 3.1">🔗</a></div>
+</div></details></div>
+<div class="workspace" data-space="1in"></div>
+<div class="autopermalink" data-description="Worksheet Exercise 3"><a href="#quiz-03-4-1" title="Copy heading and permalink for Worksheet Exercise 3" aria-label="Copy heading and permalink for Worksheet Exercise 3">🔗</a></div></article><figure class="table table-like" id="quiz-03-4-2"><figcaption><span class="type">Table</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">126<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="process-math">\(\Phi(z)\)</span> Values<div class="autopermalink" data-description="Table 126: \Phi(z) Values"><a href="#quiz-03-4-2" title="Copy heading and permalink for Table 126: \Phi(z) Values" aria-label="Copy heading and permalink for Table 126: \Phi(z) Values">🔗</a></div></figcaption><div class="tabular-box natural-width"><table class="tabular">
+<tr class="header-horizontal">
+<th scope="col" class="c m b1 r0 l0 t0 lines"><span class="process-math">\(z\)</span></th>
+<th scope="col" class="c m b1 r0 l0 t0 lines">0.00</th>
+<th scope="col" class="c m b1 r0 l0 t0 lines">0.01</th>
+<th scope="col" class="c m b1 r0 l0 t0 lines">0.02</th>
+<th scope="col" class="c m b1 r0 l0 t0 lines">0.03</th>
+<th scope="col" class="c m b1 r0 l0 t0 lines">0.04</th>
+<th scope="col" class="c m b1 r0 l0 t0 lines">0.05</th>
+<th scope="col" class="c m b1 r0 l0 t0 lines">0.06</th>
+<th scope="col" class="c m b1 r0 l0 t0 lines">0.07</th>
+<th scope="col" class="c m b1 r0 l0 t0 lines">0.08</th>
+<th scope="col" class="c m b1 r0 l0 t0 lines">0.09</th>
+</tr>
+<tr>
+<td class="c m b0 r0 l0 t0 lines">−1.6</td>
+<td class="c m b0 r0 l0 t0 lines">0.0548</td>
+<td class="c m b0 r0 l0 t0 lines">0.0537</td>
+<td class="c m b0 r0 l0 t0 lines">0.0526</td>
+<td class="c m b0 r0 l0 t0 lines">0.0516</td>
+<td class="c m b0 r0 l0 t0 lines">0.0505</td>
+<td class="c m b0 r0 l0 t0 lines">0.0495</td>
+<td class="c m b0 r0 l0 t0 lines">0.0485</td>
+<td class="c m b0 r0 l0 t0 lines">0.0475</td>
+<td class="c m b0 r0 l0 t0 lines">0.0465</td>
+<td class="c m b0 r0 l0 t0 lines">0.0455</td>
+</tr>
+<tr>
+<td class="c m b0 r0 l0 t0 lines">−1.5</td>
+<td class="c m b0 r0 l0 t0 lines">0.0668</td>
+<td class="c m b0 r0 l0 t0 lines">0.0655</td>
+<td class="c m b0 r0 l0 t0 lines">0.0643</td>
+<td class="c m b0 r0 l0 t0 lines">0.0630</td>
+<td class="c m b0 r0 l0 t0 lines">0.0618</td>
+<td class="c m b0 r0 l0 t0 lines">0.0606</td>
+<td class="c m b0 r0 l0 t0 lines">0.0594</td>
+<td class="c m b0 r0 l0 t0 lines">0.0582</td>
+<td class="c m b0 r0 l0 t0 lines">0.0571</td>
+<td class="c m b0 r0 l0 t0 lines">0.0559</td>
+</tr>
+<tr>
+<td class="c m b0 r0 l0 t0 lines">−1.4</td>
+<td class="c m b0 r0 l0 t0 lines">0.0808</td>
+<td class="c m b0 r0 l0 t0 lines">0.0793</td>
+<td class="c m b0 r0 l0 t0 lines">0.0778</td>
+<td class="c m b0 r0 l0 t0 lines">0.0764</td>
+<td class="c m b0 r0 l0 t0 lines">0.0749</td>
+<td class="c m b0 r0 l0 t0 lines">0.0735</td>
+<td class="c m b0 r0 l0 t0 lines">0.0721</td>
+<td class="c m b0 r0 l0 t0 lines">0.0708</td>
+<td class="c m b0 r0 l0 t0 lines">0.0694</td>
+<td class="c m b0 r0 l0 t0 lines">0.0681</td>
+</tr>
+<tr>
+<td class="c m b0 r0 l0 t0 lines">−1.3</td>
+<td class="c m b0 r0 l0 t0 lines">0.0968</td>
+<td class="c m b0 r0 l0 t0 lines">0.0951</td>
+<td class="c m b0 r0 l0 t0 lines">0.0934</td>
+<td class="c m b0 r0 l0 t0 lines">0.0918</td>
+<td class="c m b0 r0 l0 t0 lines">0.0901</td>
+<td class="c m b0 r0 l0 t0 lines">0.0885</td>
+<td class="c m b0 r0 l0 t0 lines">0.0869</td>
+<td class="c m b0 r0 l0 t0 lines">0.0853</td>
+<td class="c m b0 r0 l0 t0 lines">0.0838</td>
+<td class="c m b0 r0 l0 t0 lines">0.0823</td>
+</tr>
+<tr>
+<td class="c m b1 r0 l0 t0 lines">−1.2</td>
+<td class="c m b1 r0 l0 t0 lines">0.1151</td>
+<td class="c m b1 r0 l0 t0 lines">0.1131</td>
+<td class="c m b1 r0 l0 t0 lines">0.1112</td>
+<td class="c m b1 r0 l0 t0 lines">0.1093</td>
+<td class="c m b1 r0 l0 t0 lines">0.1075</td>
+<td class="c m b1 r0 l0 t0 lines">0.1056</td>
+<td class="c m b1 r0 l0 t0 lines">0.1038</td>
+<td class="c m b1 r0 l0 t0 lines">0.1020</td>
+<td class="c m b1 r0 l0 t0 lines">0.1003</td>
+<td class="c m b1 r0 l0 t0 lines">0.0985</td>
+</tr>
+<tr>
+<td class="c m b0 r0 l0 t0 lines">0.2</td>
+<td class="c m b0 r0 l0 t0 lines">0.5793</td>
+<td class="c m b0 r0 l0 t0 lines">0.5832</td>
+<td class="c m b0 r0 l0 t0 lines">0.5871</td>
+<td class="c m b0 r0 l0 t0 lines">0.5910</td>
+<td class="c m b0 r0 l0 t0 lines">0.5948</td>
+<td class="c m b0 r0 l0 t0 lines">0.5987</td>
+<td class="c m b0 r0 l0 t0 lines">0.6026</td>
+<td class="c m b0 r0 l0 t0 lines">0.6064</td>
+<td class="c m b0 r0 l0 t0 lines">0.6103</td>
+<td class="c m b0 r0 l0 t0 lines">0.6141</td>
+</tr>
+<tr>
+<td class="c m b0 r0 l0 t0 lines">0.3</td>
+<td class="c m b0 r0 l0 t0 lines">0.6179</td>
+<td class="c m b0 r0 l0 t0 lines">0.6217</td>
+<td class="c m b0 r0 l0 t0 lines">0.6255</td>
+<td class="c m b0 r0 l0 t0 lines">0.6293</td>
+<td class="c m b0 r0 l0 t0 lines">0.6331</td>
+<td class="c m b0 r0 l0 t0 lines">0.6368</td>
+<td class="c m b0 r0 l0 t0 lines">0.6406</td>
+<td class="c m b0 r0 l0 t0 lines">0.6443</td>
+<td class="c m b0 r0 l0 t0 lines">0.6480</td>
+<td class="c m b0 r0 l0 t0 lines">0.6517</td>
+</tr>
+<tr>
+<td class="c m b0 r0 l0 t0 lines">0.4</td>
+<td class="c m b0 r0 l0 t0 lines">0.6554</td>
+<td class="c m b0 r0 l0 t0 lines">0.6591</td>
+<td class="c m b0 r0 l0 t0 lines">0.6628</td>
+<td class="c m b0 r0 l0 t0 lines">0.6664</td>
+<td class="c m b0 r0 l0 t0 lines">0.6700</td>
+<td class="c m b0 r0 l0 t0 lines">0.6736</td>
+<td class="c m b0 r0 l0 t0 lines">0.6772</td>
+<td class="c m b0 r0 l0 t0 lines">0.6808</td>
+<td class="c m b0 r0 l0 t0 lines">0.6844</td>
+<td class="c m b0 r0 l0 t0 lines">0.6879</td>
+</tr>
+<tr>
+<td class="c m b0 r0 l0 t0 lines">0.5</td>
+<td class="c m b0 r0 l0 t0 lines">0.6915</td>
+<td class="c m b0 r0 l0 t0 lines">0.6950</td>
+<td class="c m b0 r0 l0 t0 lines">0.6985</td>
+<td class="c m b0 r0 l0 t0 lines">0.7019</td>
+<td class="c m b0 r0 l0 t0 lines">0.7054</td>
+<td class="c m b0 r0 l0 t0 lines">0.7088</td>
+<td class="c m b0 r0 l0 t0 lines">0.7123</td>
+<td class="c m b0 r0 l0 t0 lines">0.7157</td>
+<td class="c m b0 r0 l0 t0 lines">0.7190</td>
+<td class="c m b0 r0 l0 t0 lines">0.7224</td>
+</tr>
+<tr>
+<td class="c m b0 r0 l0 t0 lines">0.6</td>
+<td class="c m b0 r0 l0 t0 lines">0.7257</td>
+<td class="c m b0 r0 l0 t0 lines">0.7291</td>
+<td class="c m b0 r0 l0 t0 lines">0.7324</td>
+<td class="c m b0 r0 l0 t0 lines">0.7357</td>
+<td class="c m b0 r0 l0 t0 lines">0.7389</td>
+<td class="c m b0 r0 l0 t0 lines">0.7422</td>
+<td class="c m b0 r0 l0 t0 lines">0.7454</td>
+<td class="c m b0 r0 l0 t0 lines">0.7486</td>
+<td class="c m b0 r0 l0 t0 lines">0.7517</td>
+<td class="c m b0 r0 l0 t0 lines">0.7549</td>
+</tr>
+</table></div></figure></section><div class="autopermalink" data-description="Worksheet: Quiz 3"><a href="#quiz-03" title="Copy heading and permalink for Worksheet: Quiz 3" aria-label="Copy heading and permalink for Worksheet: Quiz 3">🔗</a></div></section>
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course/quizzes.html

@@ -250,6 +250,7 @@ eBookConfig.enable_chatcodes =  false;
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@@ -277,6 +278,7 @@ eBookConfig.enable_chatcodes =  false;
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+<li><a href="quiz-03.html" class="internal"><span class="title">Quiz 3</span></a></li>
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course/recitation-calculus-review.html

@@ -250,6 +250,7 @@ eBookConfig.enable_chatcodes =  false;
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@@ -347,7 +348,7 @@ eBookConfig.enable_chatcodes =  false;
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-<span class="type">Theorem</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">126</span><span class="period heading-divison-mark heading-divison-mark__period">.</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Fundamental Theorem of Calculus.</span>
+<span class="type">Theorem</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">127</span><span class="period heading-divison-mark heading-divison-mark__period">.</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Fundamental Theorem of Calculus.</span>
 </h3>
 <div class="para logical" id="thm-FTC-2-1">
 <div class="para">If <span class="process-math">\(F(x)\)</span> is an antiderivative of <span class="process-math">\(f(x)\)</span>—i.e., if <span class="process-math">\(F'(x) = f(x)\)</span>—then:</div>
@@ -358,7 +359,7 @@ eBookConfig.enable_chatcodes =  false;
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 </div>
-<div class="autopermalink" data-description="Theorem 126: Fundamental Theorem of Calculus"><a href="#thm-FTC" title="Copy heading and permalink for Theorem 126: Fundamental Theorem of Calculus" aria-label="Copy heading and permalink for Theorem 126: Fundamental Theorem of Calculus">🔗</a></div></article><div class="para" id="recitation-calculus-review-4-2">If <span class="process-math">\(f(x)\)</span> is a probability density function (don’t worry about what that means for now), then integrals such as <span class="process-math">\(\int_a^b f(x)\ dx\)</span> are used to calculate certain probabilities, as are values of the form <span class="process-math">\(F(x)\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#recitation-calculus-review-4-2" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+<div class="autopermalink" data-description="Theorem 127: Fundamental Theorem of Calculus"><a href="#thm-FTC" title="Copy heading and permalink for Theorem 127: Fundamental Theorem of Calculus" aria-label="Copy heading and permalink for Theorem 127: Fundamental Theorem of Calculus">🔗</a></div></article><div class="para" id="recitation-calculus-review-4-2">If <span class="process-math">\(f(x)\)</span> is a probability density function (don’t worry about what that means for now), then integrals such as <span class="process-math">\(\int_a^b f(x)\ dx\)</span> are used to calculate certain probabilities, as are values of the form <span class="process-math">\(F(x)\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#recitation-calculus-review-4-2" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
 </div>
 <article class="exercise exercise-like" id="recitation-calculus-review-4-3"><h3 class="heading"><span class="codenumber">5<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h3>
 <div class="introduction" id="recitation-calculus-review-4-3-1"><div class="para" id="recitation-calculus-review-4-3-1-1">Practice with the following integrals:<div class="autopermalink" data-description="Paragraph"><a href="#recitation-calculus-review-4-3-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>

course/recitations.html

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course/review.html

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course/root-1-2.html

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course/syllabus.html

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