Solution Found!
Solved: In Example 5.4 and Exercise 5.5, we considered the
Chapter 5, Problem 49E(choose chapter or problem)
In Example 5.4 and Exercise 5.5, we considered the joint density of \(Y_{1}\), the proportion of the capacity of the tank that is stocked at the beginning of the week and \(Y_{2}\), the proportion of the capacity sold during the week, given by
\(f\left(y_{1}, y_{2}\right)=\left\{\begin{array}{ll}
3 y_{1}, & 0 \leq y_{2} \leq y_{1} \leq 1, \\
0, & \text { elsewhere. }
\end{array}\right.
\)
Show that \(Y_{1}\) and \(Y_{2}\) are dependent.
Equation Transcription:
Text Transcription:
Y_1
Y_2
f(y_1,y_2)={_0, elsewhere. ^3y_1, 0</=y_2</=y_1</=1,
Y_1
Y_2
Questions & Answers
QUESTION:
In Example 5.4 and Exercise 5.5, we considered the joint density of \(Y_{1}\), the proportion of the capacity of the tank that is stocked at the beginning of the week and \(Y_{2}\), the proportion of the capacity sold during the week, given by
\(f\left(y_{1}, y_{2}\right)=\left\{\begin{array}{ll}
3 y_{1}, & 0 \leq y_{2} \leq y_{1} \leq 1, \\
0, & \text { elsewhere. }
\end{array}\right.
\)
Show that \(Y_{1}\) and \(Y_{2}\) are dependent.
Equation Transcription:
Text Transcription:
Y_1
Y_2
f(y_1,y_2)={_0, elsewhere. ^3y_1, 0</=y_2</=y_1</=1,
Y_1
Y_2
ANSWER:
Solution:
Step 1 of 2:
The proportion of the capacity sold during the week is given by,
The claim is to check and
are independent.