Answer: In Exercise 5.3, we determined that the joint

QUESTION:

In Exercise 5.3, we determined that the joint probability distribution of \(Y_{1}\), the number of married executives, and \(Y_{2}\), 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, \(0 \leq y_{1} \leq 3\), \(0 \leq y_{2} \leq 3\), and \(1 \leq y_{1}+y_{2} \leq 3\). Find the expected number of married executives among the three selected for promotion. (See Exercise 5.21.)

Equation Transcription:

Text Transcription:

Y_1

Y_2

p(y_1,y_2)=(_y_1 ^4)(_y_2 ^3)(_3-y1-y2       ^2) over (_3 ^9)

y_1

y_2

0</=y_1</=3

0</=y_2</=3

1</=y_1+y_2</=3