I have a statistics question and have calculated the part (a) answer. But I have no idea on part (b) as i have the no clue on $E(XY)$ to calculate the cov($X$.$Y$). I write to seek for advice on part (b). Please find below for the details and my calculation on part (a).
Let X and Y be random variables with $E(X|Y)=2Y$, Var($X$|$Y$)=$6Y$$2$, $E(Y)=7$, Var($Y$)$=10$.
(a) Find the mean and variance of X.
(b) Find the correlation coefficient between X and Y.
Ans for (a)
Please help to advise the part (b) solution. Thanks!