So I have got 2 variables, $A$ and $B$. I know for a fact that $E(A)$ = 0.
I don't know if they are independent.
$$Cov(A, B) = E(A B) - E(B) E(A)$$
I know that $E(A) = 0$.
Does that mean $E(A B) = 0$, too?
(I'm doing this question where I have to show the covariance between estimated residuals and each of the regressors must always be zero, ).