Let $X$ and $Y$ have the joint pdf $f(x;y)=2\exp(x+y)$, $0 < x < y < \infty$, zero elsewhere. Find the conditional mean $E(Y|X=x)$.
This seems like a simple problem. I know I have to find the marginal pdf of $x$ and then divide the joint pdf by the marginal pdf. But the marginal pdf of $X$ diverges, so I don't know how to proceed.