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andy
2026-02-05 10:24:20 -05:00
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commit a3aef1848e
4 changed files with 13 additions and 31 deletions
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course/index.html
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<html> <html>
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<!--* on 2026-02-05T07:22:54-05:00 *--> <!--* on 2026-02-05T10:22:20-05:00 *-->
<!--* A recent stable commit (2022-07-01): *--> <!--* A recent stable commit (2022-07-01): *-->
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course/lunr-pretext-search-index.js
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@@ -808,7 +808,7 @@ var ptx_lunr_docs = [
"type": "Worksheet", "type": "Worksheet",
"number": "", "number": "",
"title": "Quiz 2", "title": "Quiz 2",
"body": " Quiz 2 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. Let be integers with . Then . True. Suppose is a continuous random variable with pdf and cdf . Then . True. Suppose is a random variable taking values between 0 and 6. Then . False. Consider the joint distribution for and below. Joint Distribution 0.1 0.05 0.1 0.3 0.15 0.3 Find the marginal distributions for and . Are and independent? Since , and are not independent. Suppose a continuous random variable taking values in has cdf . Find the pdf . Find . " "body": " Quiz 2 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. Let be integers with . Then . True. Suppose is a continuous random variable with pdf and cdf . Then . True. Suppose is a random variable taking values between 0 and 6. Then . False. Consider the joint distribution for and below. Joint Distribution 0.1 0.05 0.1 0.3 0.15 0.3 Find the marginal distributions for and . Are and independent? , and . Since , and are not independent. Suppose a continuous random variable taking values in has cdf . Find the pdf . Find . "
}, },
{ {
"id": "quiz-02-3-1", "id": "quiz-02-3-1",
@@ -826,7 +826,7 @@ var ptx_lunr_docs = [
"type": "Worksheet Exercise", "type": "Worksheet Exercise",
"number": "2", "number": "2",
"title": "", "title": "",
"body": " Consider the joint distribution for and below. Joint Distribution 0.1 0.05 0.1 0.3 0.15 0.3 Find the marginal distributions for and . Are and independent? Since , and are not independent. " "body": " Consider the joint distribution for and below. Joint Distribution 0.1 0.05 0.1 0.3 0.15 0.3 Find the marginal distributions for and . Are and independent? , and . Since , and are not independent. "
}, },
{ {
"id": "quiz-02-4-1", "id": "quiz-02-4-1",
course/quiz-02-printable.html
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@@ -309,11 +309,9 @@ eBookConfig.enable_chatcodes = false;
<div class="para logical" id="quiz-02-3-2-2-2-1"> <div class="para logical" id="quiz-02-3-2-2-2-1">
<div class="displaymath process-math" id="quiz-02-3-2-2-2-1-1"> <div class="displaymath process-math" id="quiz-02-3-2-2-2-1-1">
\begin{align*} \begin{align*}
\Pr(X = 0) \amp = 0.1 + 0.3 = 0.4 \\ \Pr(X = 0) \amp = 0.1 + 0.3 = 0.4 \amp \Pr(Y = 0) \amp = 0.1 + 0.05 + 0.1 = 0.25 \\
\Pr(X = 1) \amp = 0.05 + 0.15 = 0.2 \\ \Pr(X = 1) \amp = 0.05 + 0.15 = 0.2 \amp \Pr(Y = 1) \amp = 0.3 + 0.15 + 0.3 = 0.75 \\
\Pr(X = 2) \amp = 0.1 + 0.3 = 0.4 \\ \Pr(X = 2) \amp = 0.1 + 0.3 = 0.4
\Pr(Y = 0) \amp = 0.1 + 0.05 + 0.1 = 0.25 \\
\Pr(Y = 1) \amp = 0.3 + 0.15 + 0.3 = 0.75
\end{align*} \end{align*}
</div> </div>
<div class="autopermalink" data-description="Paragraph"><a href="#quiz-02-3-2-2-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div> <div class="autopermalink" data-description="Paragraph"><a href="#quiz-02-3-2-2-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
@@ -324,15 +322,8 @@ eBookConfig.enable_chatcodes = false;
<div class="para" id="quiz-02-3-2-3-1-1">Are <span class="process-math">\(X\)</span> and <span class="process-math">\(Y\)</span> independent?<div class="autopermalink" data-description="Paragraph"><a href="#quiz-02-3-2-3-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div> <div class="para" id="quiz-02-3-2-3-1-1">Are <span class="process-math">\(X\)</span> and <span class="process-math">\(Y\)</span> independent?<div class="autopermalink" data-description="Paragraph"><a href="#quiz-02-3-2-3-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
</div> </div>
<div class="solutions"><details id="quiz-02-3-2-3-2" class="solution solution-like born-hidden-knowl"><summary class="knowl__link"><span class="type">Solution</span><span class="period heading-divison-mark heading-divison-mark__period">.</span></summary><div class="solution solution-like knowl__content"> <div class="solutions"><details id="quiz-02-3-2-3-2" class="solution solution-like born-hidden-knowl"><summary class="knowl__link"><span class="type">Solution</span><span class="period heading-divison-mark heading-divison-mark__period">.</span></summary><div class="solution solution-like knowl__content">
<div class="para logical" id="quiz-02-3-2-3-2-1"> <div class="para" id="quiz-02-3-2-3-2-1">
<div class="displaymath process-math" id="quiz-02-3-2-3-2-1-1"> <span class="process-math">\(\Pr(X = 2, Y = 0) = 0.2 \text{,}\)</span> and <span class="process-math">\(\Pr(X = 2)\Pr(Y = 0) = (0.4)(0.25) = 0.1\text{.}\)</span> Since <span class="process-math">\(0.2 \neq 0.1\text{,}\)</span> <span class="process-math">\(X\)</span> and <span class="process-math">\(Y\)</span> are not independent.<div class="autopermalink" data-description="Paragraph"><a href="#quiz-02-3-2-3-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
\begin{align*}
\Pr(X = 2, Y = 0) \amp = 0.2 \\
\Pr(X = 2)\Pr(Y = 0) \amp = (0.4)(0.25) = 0.1
\end{align*}
</div>
<div class="para">Since <span class="process-math">\(0.2 \neq 0.1\text{,}\)</span> <span class="process-math">\(X\)</span> and <span class="process-math">\(Y\)</span> are not independent.</div>
<div class="autopermalink" data-description="Paragraph"><a href="#quiz-02-3-2-3-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
</div> </div>
<div class="autopermalink" data-description="Solution 2.b.1"><a href="#quiz-02-3-2-3-2" title="Copy heading and permalink for Solution 2.b.1" aria-label="Copy heading and permalink for Solution 2.b.1">🔗</a></div> <div class="autopermalink" data-description="Solution 2.b.1"><a href="#quiz-02-3-2-3-2" title="Copy heading and permalink for Solution 2.b.1" aria-label="Copy heading and permalink for Solution 2.b.1">🔗</a></div>
</div></details></div> </div></details></div>
course/quiz-02.html
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@@ -294,11 +294,9 @@ eBookConfig.enable_chatcodes = false;
<div class="para logical" id="quiz-02-3-2-2-2-1"> <div class="para logical" id="quiz-02-3-2-2-2-1">
<div class="displaymath process-math" id="quiz-02-3-2-2-2-1-1"> <div class="displaymath process-math" id="quiz-02-3-2-2-2-1-1">
\begin{align*} \begin{align*}
\Pr(X = 0) \amp = 0.1 + 0.3 = 0.4 \\ \Pr(X = 0) \amp = 0.1 + 0.3 = 0.4 \amp \Pr(Y = 0) \amp = 0.1 + 0.05 + 0.1 = 0.25 \\
\Pr(X = 1) \amp = 0.05 + 0.15 = 0.2 \\ \Pr(X = 1) \amp = 0.05 + 0.15 = 0.2 \amp \Pr(Y = 1) \amp = 0.3 + 0.15 + 0.3 = 0.75 \\
\Pr(X = 2) \amp = 0.1 + 0.3 = 0.4 \\ \Pr(X = 2) \amp = 0.1 + 0.3 = 0.4
\Pr(Y = 0) \amp = 0.1 + 0.05 + 0.1 = 0.25 \\
\Pr(Y = 1) \amp = 0.3 + 0.15 + 0.3 = 0.75
\end{align*} \end{align*}
</div> </div>
<div class="autopermalink" data-description="Paragraph"><a href="#quiz-02-3-2-2-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div> <div class="autopermalink" data-description="Paragraph"><a href="#quiz-02-3-2-2-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
@@ -309,15 +307,8 @@ eBookConfig.enable_chatcodes = false;
<div class="para" id="quiz-02-3-2-3-1-1">Are <span class="process-math">\(X\)</span> and <span class="process-math">\(Y\)</span> independent?<div class="autopermalink" data-description="Paragraph"><a href="#quiz-02-3-2-3-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div> <div class="para" id="quiz-02-3-2-3-1-1">Are <span class="process-math">\(X\)</span> and <span class="process-math">\(Y\)</span> independent?<div class="autopermalink" data-description="Paragraph"><a href="#quiz-02-3-2-3-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
</div> </div>
<div class="solutions"><details id="quiz-02-3-2-3-2" class="solution solution-like born-hidden-knowl"><summary class="knowl__link"><span class="type">Solution</span><span class="period heading-divison-mark heading-divison-mark__period">.</span></summary><div class="solution solution-like knowl__content"> <div class="solutions"><details id="quiz-02-3-2-3-2" class="solution solution-like born-hidden-knowl"><summary class="knowl__link"><span class="type">Solution</span><span class="period heading-divison-mark heading-divison-mark__period">.</span></summary><div class="solution solution-like knowl__content">
<div class="para logical" id="quiz-02-3-2-3-2-1"> <div class="para" id="quiz-02-3-2-3-2-1">
<div class="displaymath process-math" id="quiz-02-3-2-3-2-1-1"> <span class="process-math">\(\Pr(X = 2, Y = 0) = 0.2 \text{,}\)</span> and <span class="process-math">\(\Pr(X = 2)\Pr(Y = 0) = (0.4)(0.25) = 0.1\text{.}\)</span> Since <span class="process-math">\(0.2 \neq 0.1\text{,}\)</span> <span class="process-math">\(X\)</span> and <span class="process-math">\(Y\)</span> are not independent.<div class="autopermalink" data-description="Paragraph"><a href="#quiz-02-3-2-3-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
\begin{align*}
\Pr(X = 2, Y = 0) \amp = 0.2 \\
\Pr(X = 2)\Pr(Y = 0) \amp = (0.4)(0.25) = 0.1
\end{align*}
</div>
<div class="para">Since <span class="process-math">\(0.2 \neq 0.1\text{,}\)</span> <span class="process-math">\(X\)</span> and <span class="process-math">\(Y\)</span> are not independent.</div>
<div class="autopermalink" data-description="Paragraph"><a href="#quiz-02-3-2-3-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
</div> </div>
<div class="autopermalink" data-description="Solution 2.b.1"><a href="#quiz-02-3-2-3-2" title="Copy heading and permalink for Solution 2.b.1" aria-label="Copy heading and permalink for Solution 2.b.1">🔗</a></div> <div class="autopermalink" data-description="Solution 2.b.1"><a href="#quiz-02-3-2-3-2" title="Copy heading and permalink for Solution 2.b.1" aria-label="Copy heading and permalink for Solution 2.b.1">🔗</a></div>
</div></details></div> </div></details></div>