I have a random variable $\displaystyle U,$ which has a uniform distribution with parameters 0 and 2. I have another random variable $\displaystyle X$, which has a moment generating function of $\displaystyle {(1-ux)^{-1}}$ whereby $\displaystyle U=u$.

1. How do I find E(X)? Do I simply differentiate the mgf? [SOLVED]

2. How do I find $\displaystyle E(X|U)$ and $\displaystyle Var(X|U)$?

Your help is very much appreciated.