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andy
2026-02-05 10:24:20 -05:00
parent 44053ec9fe
commit a3aef1848e
4 changed files with 13 additions and 31 deletions
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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="displaymath process-math" id="quiz-02-3-2-2-2-1-1">
\begin{align*}
\Pr(X = 0) \amp = 0.1 + 0.3 = 0.4 \\
\Pr(X = 1) \amp = 0.05 + 0.15 = 0.2 \\
\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
\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 \amp \Pr(Y = 1) \amp = 0.3 + 0.15 + 0.3 = 0.75 \\
\Pr(X = 2) \amp = 0.1 + 0.3 = 0.4
\end{align*}
</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>
<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="displaymath process-math" id="quiz-02-3-2-3-2-1-1">
\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 class="para" id="quiz-02-3-2-3-2-1">
<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>
</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>