I have problem figuring out the solution for this task:
X1 and X2 are independent random variables with normal distribution ~N(2,1). What is a covariance of $X_1 − 4X_2^2$ and $X_1 + X_2$.
So far I've managed to come up with this:
$cov(X_1 − 4X_2^2$ , $X_1 + X_2) = cov(X_1, X_1) - cov(X_1,X_2)-4cov(X_1, X_2^2) - 4cov(X_2, X_2^2) = Var(X_1) + 0 -4cov(X_1, X_2^2) - 4cov(X_2, X_2^2)$
But I don't know how to handle both $cov(X_1, X_2^2)$ and $cov(X_2, X_2^2)$. X1 and X2 are independent, but does it mean that $X_1$ and $X_2^2$ are independent too? What about $X_2$ and $X_2^2$?