Let X and Y be random variables with $\displaystyle p(x,y)=e^ {-y} $ for $\displaystyle 0<x<y<+ \infty $

Compute $\displaystyle E[X | Y ] $ and $\displaystyle E[Y | X ] $

My solution:

For $\displaystyle E[X | Y ] $, I have $\displaystyle \int x p(x | y) dx = \int x \frac {p(x,y)}{p(y)} dx $

$\displaystyle = \int x \frac {e^{-y}}{p(y)} dx $

But I'm stuck here because I don't know what p(y) is.

Any help is appreciated, thank you!