I am given two random variables $Y_1$ and $Y_2$ and:
- $E(Y_1) = 4$
- $E(Y_2) = -1$
- $V(Y_1) = 2$
- $V(Y_2) = 8$
I am asked to find $Cov(Y_1,Y_1)$
I know $Cov(Y_1,Y_2) = E(Y_1Y_2)-E(Y_1)E(Y_2)$
I'm not sure if it is a typo, but it says $Cov(Y_1,Y_1)$ NOT $Cov(Y_1,Y_2)$
The answer is $2$, but i'm not sure how to get $E(Y_1Y_2)$ from the information given, or why it's asking for the Cov of the same variable?
Thanks for any help!
Best Answer
$cov(Y_1,Y_1)=var(Y_1)=2$ This follows from the definition of covariance:
$cov(Y_1,Y_1)=E(Y_1\cdot Y_1)-E(Y_1)E(Y_1)=E(Y_1^2)-E(Y_1)^2$