Solution Found!
Solution: In Exercise 5.3, we determined that the joint
Chapter 5, Problem 90E(choose chapter or problem)
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
\(p\left(y_{1,} y_{2}\right)=\frac{\left(\begin{array}{l}4 \\y_{1}\end{array}\right)\left(\begin{array}{l}3 \\y_{2}\end{array}\right)\left(\begin{array}{l}2 \\3-y_{1}=y_{2}\end{array}\right)}{\left({}_{3}^{9}\right)}\)
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 \(\operatorname{Cov}\left(Y_{1}, Y_{2}\right)\).
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)/_3 ^9
y_1
y_2
0 leq y_1 leq 3,0 leq y_2 leq 3
1 leq y_1+y_2 leq 3
Cov(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 \(Y_{2}\), the number of never-married executives, is given by
\(p\left(y_{1,} y_{2}\right)=\frac{\left(\begin{array}{l}4 \\y_{1}\end{array}\right)\left(\begin{array}{l}3 \\y_{2}\end{array}\right)\left(\begin{array}{l}2 \\3-y_{1}=y_{2}\end{array}\right)}{\left({}_{3}^{9}\right)}\)
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 \(\operatorname{Cov}\left(Y_{1}, Y_{2}\right)\).
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)/_3 ^9
y_1
y_2
0 leq y_1 leq 3,0 leq y_2 leq 3
1 leq y_1+y_2 leq 3
Cov(Y_1,Y_2)
ANSWER:
Solution:
Step 1 of 3:
It is given that in a firm there are 9 executives out of which 4 are married,3 are unmarried and 2 are divorced.
denotes the number of married executives and
denotes the number of unmarried executes.
Also, it is given that 3 executives are selected at random for promotion.
The joint probability distribution of and
is given as
P(,
)=
,0
Using this we need to find the Cov(,
).