Solution Found!
Solved: In Exercise 5.9, we determined that is a valid
Chapter 5, Problem 53E(choose chapter or problem)
In Exercise 5.9, we determined that
\(f\left(y_{1}, y_{2}\right)=\left\{\begin{array}{ll}
6\left(1-y_{2}\right), & 0 \leq y_{1} \leq y_{2} \leq 1, \\
0, & \text { elsewhere }
\end{array}\right.
\)
is a valid joint probability density function. Are \(Y_{1}\) and \(Y_{2}\) independent?
Equation Transcription:
Text Transcription:
f(y_1,y_2)={_0, elsewhere ^6(1-y_2), 0</=y_1</=y_2</=1,
Y_1
Y_2
Questions & Answers
QUESTION:
In Exercise 5.9, we determined that
\(f\left(y_{1}, y_{2}\right)=\left\{\begin{array}{ll}
6\left(1-y_{2}\right), & 0 \leq y_{1} \leq y_{2} \leq 1, \\
0, & \text { elsewhere }
\end{array}\right.
\)
is a valid joint probability density function. Are \(Y_{1}\) and \(Y_{2}\) independent?
Equation Transcription:
Text Transcription:
f(y_1,y_2)={_0, elsewhere ^6(1-y_2), 0</=y_1</=y_2</=1,
Y_1
Y_2
ANSWER:
Answer:
Step 1 of 1:
In Exercise we determined that
Is a valid joint probability density function.
We need to find whether are independent or not.
If are continuous random variables with joint density function
and marginal density functions respectively, then
are independent if and only if
……………..(1)
For all pairs of real numbers