Conditional Mathematical Expectation (problem) Given that $X \sim CUD(0,1)$ and $Y \sim CUD(0,X)$, where CUD means continous uniform distribution, what is $E(X|Y)$ ? I can't find density function $f(x,y)$. Am I missing something obvious?

Answer by kjetil b halvorsen.

I suppose that you mean to say $Y|X = x \sim CUD(0,x)$. Then the density of $X$ is $f(x)=1_{0