Solution Found!
Refer to Exercises 5.6, 5.24, and 5.50. Suppose that a
Chapter 5, Problem 74E(choose chapter or problem)
Refer to Exercises , and
. Suppose that a radioactive particle is randomly located in a square with sides of unit length. A reasonable model for the joint density function for \(Y_{1}\) and \(Y_{2}\) is
\(f\left(y_{1}, y_{2}\right)=\left\{\begin{array}{ll}
1, & 0 \leq y_{1} \leq 1,0 \leq y_{2} \leq 1, \\
0, & \text { elsewhere. }
\end{array}\right.
\)
a What is \(E\left(Y_{1}-Y_{2}\right)\)?
b What is \(E\left(Y_{1} Y_{2}\right)\)?
c What is \(E\left(Y_{1}^{2}+Y_{2}^{2}\right)\)?
d What is \(V\left(Y_{1} Y_{2}\right)\)?
Equation Transcription:
Text Transcription:
Y_1
Y_2
f(y_1,y_2)={_0, elsewhere. ^1, 0</=y_1</=1,0</=y_2</=1,
E(Y_1-Y_2)
E(Y_1Y_2)
E(Y_1^2+Y_2^2)
V(Y_1Y_2)
Questions & Answers
QUESTION:
Refer to Exercises , and
. Suppose that a radioactive particle is randomly located in a square with sides of unit length. A reasonable model for the joint density function for \(Y_{1}\) and \(Y_{2}\) is
\(f\left(y_{1}, y_{2}\right)=\left\{\begin{array}{ll}
1, & 0 \leq y_{1} \leq 1,0 \leq y_{2} \leq 1, \\
0, & \text { elsewhere. }
\end{array}\right.
\)
a What is \(E\left(Y_{1}-Y_{2}\right)\)?
b What is \(E\left(Y_{1} Y_{2}\right)\)?
c What is \(E\left(Y_{1}^{2}+Y_{2}^{2}\right)\)?
d What is \(V\left(Y_{1} Y_{2}\right)\)?
Equation Transcription:
Text Transcription:
Y_1
Y_2
f(y_1,y_2)={_0, elsewhere. ^1, 0</=y_1</=1,0</=y_2</=1,
E(Y_1-Y_2)
E(Y_1Y_2)
E(Y_1^2+Y_2^2)
V(Y_1Y_2)
ANSWER:
Solution:
Step 1 of 5:
The Radioactive particle is randomly located in a square with sides of unit length.
The joint density function for and
is
