Joint Density & Expectations for 1/y If X and Y have joint density function:
$f(x,y) = \frac1y$ for $0 < y < 1$ and $0 < x < y$; zero otherwise
Find:
a. $E[XY]$

b. $E[X]$

c. $E[Y]$
c. is fine. I found the marginal density of y (which ended up being 1) and then found $E[Y]$ to be 0.5. 
b. is what is giving me trouble. When finding the marginal density of $x$, you end up with $\ln(y)$ where $y = 1$ and $y=0$. $\ln(1)$ is no problem, but $\ln$ is undefined at $y=0$. How can I calculate the marginal density of $f_X(x)$ so that I can then find $E[XY]$?
Thank you!

$$E(h(X,Y))=\iint h(x,y)f(x,y)\,\mathrm dx\,\mathrm dy=\int_0^1\frac 1 y\int_0^y h(x,y)\,\mathrm dx\,\mathrm dy=\ldots$$
