# Finding $E(XY)$ given $E(X)$, $E(Y)$, $E(Y^2)$, $E(X|Y)$

So here is what I know: \begin{align} E(X) &= 13\\ E(Y) &= 2\\ E(X|Y) &= 3y + 7\\ E(Y^2) &= 8 \end{align} How do I find $E(XY)$?

Thanks!

\begin{align} E[XY] & =E[E[XY|Y]] \\ & =E[E[X|Y]\cdot Y] \\ & =E[(3Y+7)\cdot Y] \\ & =E[3Y^2+7Y] \\ & =3E[Y^2]+7E[Y] \\ & =3\cdot 8 +7\cdot 2 \\ & =24+14 \\ &=38 \end{align}