Solution Found!
In Exercise 5.38, we determined that the joint density
Chapter 5, Problem 82E(choose chapter or problem)
In Exercise 5.38, we determined that the joint density function for \(Y_{1}\), the weight in tons of a bulk item stocked by a supplier, and \(Y_{2}\), the weight of the item sold by the supplier, has joint density
\(f\left(y_{1}, y_{2}\right)=\left\{\begin{array}{ll}
1 / y_{1}, & 0 \leq y_{2} \leq y_{1} \leq 1, \\
0, & \text { elsewhere. }
\end{array}\right.
\)
In this case, the random variable \(Y_{1}-Y_{2}\) measures the amount of stock remaining at the end of the week, a quantity of great importance to the supplier. Find \(E\left(Y_{1}-Y_{2}\right)\).
Equation Transcription:
Text Transcription:
Y_1
Y_2
f(y_1,y_2){_0, elsewhere. ^1/y_1, 0</=y_2</=y_1</=1,
Y_1-Y_2
E(Y_1-Y_2)
Questions & Answers
QUESTION:
In Exercise 5.38, we determined that the joint density function for \(Y_{1}\), the weight in tons of a bulk item stocked by a supplier, and \(Y_{2}\), the weight of the item sold by the supplier, has joint density
\(f\left(y_{1}, y_{2}\right)=\left\{\begin{array}{ll}
1 / y_{1}, & 0 \leq y_{2} \leq y_{1} \leq 1, \\
0, & \text { elsewhere. }
\end{array}\right.
\)
In this case, the random variable \(Y_{1}-Y_{2}\) measures the amount of stock remaining at the end of the week, a quantity of great importance to the supplier. Find \(E\left(Y_{1}-Y_{2}\right)\).
Equation Transcription:
Text Transcription:
Y_1
Y_2
f(y_1,y_2){_0, elsewhere. ^1/y_1, 0</=y_2</=y_1</=1,
Y_1-Y_2
E(Y_1-Y_2)
ANSWER:
Answer:
Step 1 of 1:
In Exercise we determined that the joint density function for
the weight in tons of a bulk item stocked by a supplier, and
the weight of the item sold by the supplier, has joint density
In this case, the random variable measures the amount of stock remaining.
We need to find the value of
We can write as,
T