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Solved: In Exercise 5.6, we assumed that if a radioactive
Chapter 5, Problem 50E(choose chapter or problem)
In Exercise 5.6, we assumed that if 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. Are \(Y_{1}\) and \(Y_{2}\) independent?
b. Does the result from part (a) explain the results you obtained in Exercise 5.24 (d)–(f)? Why?
Equation Transcription:
Text Transcription:
Y_1
Y_2
f(y_1,y_2)={_0, elsewhere. ^1, 0</=y_1</=1, 0</=y_2</=1,
Y_1
Y_2
Questions & Answers
QUESTION:
In Exercise 5.6, we assumed that if 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. Are \(Y_{1}\) and \(Y_{2}\) independent?
b. Does the result from part (a) explain the results you obtained in Exercise 5.24 (d)–(f)? Why?
Equation Transcription:
Text Transcription:
Y_1
Y_2
f(y_1,y_2)={_0, elsewhere. ^1, 0</=y_1</=1, 0</=y_2</=1,
Y_1
Y_2
ANSWER:
Solution:
Step 1 of 3:
Given the joint density function for and
is
