Let $(X_1 ,Y_1) , ...(X_n ,Y_n)$ be IID and have a normal distribution with $ E(X_1)=E(Y_1)=0$ and $ var(X_1)=var(Y_1)=1$ and $Cov(X_1 ,Y_1)=\theta$.
I need to find $E(X_1^2Y_1^2)$.
Can i generalize , $Var(X) =E(X^2) - (E(X))^2$ to this ?.
I am not sure whether it is correct or not.
So in that case,
$Cov(X^2_1 ,Y^2_1)$ = $E(X_1^2Y_1^2)$ -$E(X^2_1)E(Y^2_1)$.
Then my next problem is how to find $Cov(X^2_1 ,Y^2_1)$ .
Can anyone help me figure out that ?