Solution Found!
Solved: In Exercise 5.18, Y1 and Y2 denoted the lengths of
Chapter 5, Problem 61E(choose chapter or problem)
In Exercise 5.18, \(Y_{1}\) and \(Y_{2}\) denoted the lengths of life, in hundreds of hours, for components of types I and II, respectively, in an electronic system. The joint density of \(Y_{1}\) and \(Y_{2}\) is
\(f\left(y_{1}, y_{2}\right)=\left\{\begin{array}{ll}
(1 / 8) y_{1} e^{-\left(y_{1}+y_{2}\right) / 2}, & y_{1}>0, y_{2}>0, \\
0, & \text { elsewhere. }
\end{array}\right.
\)
Are \(Y_{1}\) and \(Y_{2}\) independent?
Equation Transcription:
Text Transcription:
Y_1
Y_2
Y_1
Y_2
f(y_1,y_2)={_0, elsewhere. ^(1/8)y_1e^-(y_1+y_2)/2, y_1>0,y_2>0,
Y_1
Y_2
Questions & Answers
QUESTION:
In Exercise 5.18, \(Y_{1}\) and \(Y_{2}\) denoted the lengths of life, in hundreds of hours, for components of types I and II, respectively, in an electronic system. The joint density of \(Y_{1}\) and \(Y_{2}\) is
\(f\left(y_{1}, y_{2}\right)=\left\{\begin{array}{ll}
(1 / 8) y_{1} e^{-\left(y_{1}+y_{2}\right) / 2}, & y_{1}>0, y_{2}>0, \\
0, & \text { elsewhere. }
\end{array}\right.
\)
Are \(Y_{1}\) and \(Y_{2}\) independent?
Equation Transcription:
Text Transcription:
Y_1
Y_2
Y_1
Y_2
f(y_1,y_2)={_0, elsewhere. ^(1/8)y_1e^-(y_1+y_2)/2, y_1>0,y_2>0,
Y_1
Y_2
ANSWER:
Solution :
Step 1 of 1:
Let and
have joint density function.
Then the joint density function and
is
Our goal is:
We need to find and
are independent or not.
Now we have to find and
are independent or not.