Solution Found!
Solved: In Exercise 5.3, we determined that the joint
Chapter 5, Problem 47E(choose chapter or problem)
In Exercise 5.3, we determined that the joint probability distribution of \(Y_{1}\), the number of married executives, and \(\mathrm{Y}_{2}\), the number of never-married executives, is given by
\(p\left(y_{1}, y_{2}\right)=\frac{\left(\begin{array}{c}
4 \\
y_{1}
\end{array}\right)\left(\begin{array}{c}
3 \\
y_{2}
\end{array}\right)\left(\begin{array}{c}
2 \\
3-y_{1}-y_{2}
\end{array}\right)}{\left(\begin{array}{l}
9 \\
3
\end{array}\right)},
\)
where \(y_{1}) and \(y_{2}) are integers, \(0\le y_1\le3,\ 0\le y_2\le3\), and \(1 \leq y_{1}+y_{2} \leq 3\). Are \(Y_{1}\) and \(Y_{2}\) independent? (Recall your answer to Exercise 5.21.)
Equation Transcription:
Text Transcription:
Y_1
Y_2
p(y_1,y_2)=(_y_1 ^4)(_y_2 ^3)(_3-y_1-y_2 ^2)over( _3 ^9)
y_1
y_2
0</=y_1</=3, 0</=y_2</=3
1</=y_1+y_2</=3
Y_1
Y_2
Questions & Answers
QUESTION:
In Exercise 5.3, we determined that the joint probability distribution of \(Y_{1}\), the number of married executives, and \(\mathrm{Y}_{2}\), the number of never-married executives, is given by
\(p\left(y_{1}, y_{2}\right)=\frac{\left(\begin{array}{c}
4 \\
y_{1}
\end{array}\right)\left(\begin{array}{c}
3 \\
y_{2}
\end{array}\right)\left(\begin{array}{c}
2 \\
3-y_{1}-y_{2}
\end{array}\right)}{\left(\begin{array}{l}
9 \\
3
\end{array}\right)},
\)
where \(y_{1}) and \(y_{2}) are integers, \(0\le y_1\le3,\ 0\le y_2\le3\), and \(1 \leq y_{1}+y_{2} \leq 3\). Are \(Y_{1}\) and \(Y_{2}\) independent? (Recall your answer to Exercise 5.21.)
Equation Transcription:
Text Transcription:
Y_1
Y_2
p(y_1,y_2)=(_y_1 ^4)(_y_2 ^3)(_3-y_1-y_2 ^2)over( _3 ^9)
y_1
y_2
0</=y_1</=3, 0</=y_2</=3
1</=y_1+y_2</=3
Y_1
Y_2
ANSWER:
Solution:
Step 1 of 2:
We have joint probability distribution of and
is
p(,
) =
Where, , and
are integers,
,
and
The claim is to check and
are independent.