I am having trouble getting started in the right direction with the following problem:

Random variable X~U[0,1] and the conditional distribution of Y is Y|X=x~U[0,x], what is E[y].

This is what I have:

1.) Definition of conditional expectation

$\displaystyle

f(Y|X=x) = \frac{f_{XY} (x,y)}{f_x (x)}

$

2.) Get fx,y(x,y)

3.) get fx(x)

I know the general steps, but I don't know how to set them up. Can somebody please put these steps in working form and get me started. Thanks