Solution Found!
Solved: In Exercise 5.8, we derived the fact that
Chapter 5, Problem 91E(choose chapter or problem)
In Exercise , we derived the fact that
\(f\left(y_{1}, y_{2}\right)=\left\{\begin{array}{ll}4 y_{1} y_{2}, & & 0 \leq y_{1} \leq 1,0 \leq y_{2} \leq 1 \\0, & & \text { elsewhere }\end{array}\right.\)
Show that \operatorname \({Cov}\left(Y_{1}, Y_{2}\right)=0\). Does it surprise you that \operatorname \({Cov}\left(Y_{1}, Y_{2}\right)\) is zero? Why?
Equation Transcription:
{
Text Transcription:
f(y_1,y_2)= {_0,elsewhere ^4y_1 y_2, 0 leq y_1 leq 1,0 leq y_2 leq1,
Cov(Y_1,Y_2)=0
Cov(Y_1,Y_2)
Questions & Answers
QUESTION:
In Exercise , we derived the fact that
\(f\left(y_{1}, y_{2}\right)=\left\{\begin{array}{ll}4 y_{1} y_{2}, & & 0 \leq y_{1} \leq 1,0 \leq y_{2} \leq 1 \\0, & & \text { elsewhere }\end{array}\right.\)
Show that \operatorname \({Cov}\left(Y_{1}, Y_{2}\right)=0\). Does it surprise you that \operatorname \({Cov}\left(Y_{1}, Y_{2}\right)\) is zero? Why?
Equation Transcription:
{
Text Transcription:
f(y_1,y_2)= {_0,elsewhere ^4y_1 y_2, 0 leq y_1 leq 1,0 leq y_2 leq1,
Cov(Y_1,Y_2)=0
Cov(Y_1,Y_2)
ANSWER:
Solution:
Step 1 of 2:
It is given that and
has the joint probability density function
f()=
Using this we need to show that Cov( ,
)=0.