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Finished Quiz 2 solutions

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2026-02-05 10:23:54 -05:00
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source/quizzes/quiz-02.ptx
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<solution>
<p>
<md>
<mrow> \Pr(X = 0) \amp = 0.1 + 0.3 = 0.4 </mrow>
<mrow> \Pr(X = 1) \amp = 0.05 + 0.15 = 0.2 </mrow>
<mrow> \Pr(X = 0) \amp = 0.1 + 0.3 = 0.4 \amp \Pr(Y = 0) \amp = 0.1 + 0.05 + 0.1 = 0.25 </mrow>
<mrow> \Pr(X = 1) \amp = 0.05 + 0.15 = 0.2 \amp \Pr(Y = 1) \amp = 0.3 + 0.15 + 0.3 = 0.75 </mrow>
<mrow> \Pr(X = 2) \amp = 0.1 + 0.3 = 0.4 </mrow>
<mrow> \Pr(Y = 0) \amp = 0.1 + 0.05 + 0.1 = 0.25 </mrow>
<mrow> \Pr(Y = 1) \amp = 0.3 + 0.15 + 0.3 = 0.75 </mrow>
</md>
</p>
</solution>
@@ -142,11 +140,7 @@
<solution>
<p>
<md>
<mrow> \Pr(X = 2, Y = 0) \amp = 0.2 </mrow>
<mrow> \Pr(X = 2)\Pr(Y = 0) \amp = (0.4)(0.25) = 0.1 </mrow>
</md>
Since <m>0.2 \neq 0.1</m>, <m>X</m> and <m>Y</m> are not independent.
<m>\Pr(X = 2, Y = 0) = 0.2 </m>, and <m> \Pr(X = 2)\Pr(Y = 0) = (0.4)(0.25) = 0.1</m>. Since <m>0.2 \neq 0.1</m>, <m>X</m> and <m>Y</m> are not independent.
</p>
</solution>
</task>