diff --git a/course/index.html b/course/index.html index 7b1a005..bf48166 100755 --- a/course/index.html +++ b/course/index.html @@ -2,7 +2,7 @@ - + diff --git a/course/lunr-pretext-search-index.js b/course/lunr-pretext-search-index.js index 2420a1a..701f545 100755 --- a/course/lunr-pretext-search-index.js +++ b/course/lunr-pretext-search-index.js @@ -808,7 +808,7 @@ var ptx_lunr_docs = [ "type": "Worksheet", "number": "", "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", @@ -826,7 +826,7 @@ var ptx_lunr_docs = [ "type": "Worksheet Exercise", "number": "2", "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", diff --git a/course/quiz-02-printable.html b/course/quiz-02-printable.html index ffe1902..711b5f8 100755 --- a/course/quiz-02-printable.html +++ b/course/quiz-02-printable.html @@ -309,11 +309,9 @@ eBookConfig.enable_chatcodes = false;
\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*}
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@@ -324,15 +322,8 @@ eBookConfig.enable_chatcodes = false;
Are \(X\) and \(Y\) independent?
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Solution.
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-
-\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*} -
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Since \(0.2 \neq 0.1\text{,}\) \(X\) and \(Y\) are not independent.
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+
+\(\Pr(X = 2, Y = 0) = 0.2 \text{,}\) and \(\Pr(X = 2)\Pr(Y = 0) = (0.4)(0.25) = 0.1\text{.}\) Since \(0.2 \neq 0.1\text{,}\) \(X\) and \(Y\) are not independent.
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diff --git a/course/quiz-02.html b/course/quiz-02.html index 47022a2..f3b59f0 100755 --- a/course/quiz-02.html +++ b/course/quiz-02.html @@ -294,11 +294,9 @@ eBookConfig.enable_chatcodes = false;
\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*}
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@@ -309,15 +307,8 @@ eBookConfig.enable_chatcodes = false;
Are \(X\) and \(Y\) independent?
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Solution.
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-
-\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*} -
-
Since \(0.2 \neq 0.1\text{,}\) \(X\) and \(Y\) are not independent.
-
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+
+\(\Pr(X = 2, Y = 0) = 0.2 \text{,}\) and \(\Pr(X = 2)\Pr(Y = 0) = (0.4)(0.25) = 0.1\text{.}\) Since \(0.2 \neq 0.1\text{,}\) \(X\) and \(Y\) are not independent.
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