I have that (X, Y) are uniformly distributed in the triangle defined by the vertices $(0, 0)$, $(1, 0)$, and $(0, 1)$. I am trying to find the following expectation value:
$$ E\left( (X-Y)^2 | X \right) $$
I am able to get the joint density, marginal densities, and conditional densities fairly easily. However, I am a little confused on how to go about solving this?