Hi !

Okay, this problem has been bugging me... I guess I have some problems with conditional things

Let X and Y two independent rv's, both following a uniform distribution over [0,1]

Define $\displaystyle Z=\max\{0,Y-X\}$

Find the conditional expectation $\displaystyle \mathbb{E}[Z|X]$. Then find the conditional distribution of Z such that X=x.

hem... I was thinking about splitting the expectation and keeping the part where Y>X (since it's 0 elsewhere).

But I'm drawing a blank there

Also, is it more logical to first find the conditional distribution before the conditional expectation ?

And would someone be kind enough to give me the general guidelines when dealing with such a problem ?

Thanks for any help !