# Conditional moment generating functions

1. Sep 16, 2010

### muso07

1. The problem statement, all variables and given/known data
Random variable U is continuous uniform in the time interval (0,2)
T|U (T given U) is modelled by the mgf $$\frac{1}{1-ut}$$
Find:
a) E(U)
b) E(T|U) and Var(T|U)
c) E(T) and Var(T)

2. Relevant equations

3. The attempt at a solution
a) This one was fine, E(U)=1
b) I know E(X)=m'(0), but how does it work with conditional distributions?
c) Again, not sure how I find the marginal distribution of T from the conditional mgf.

Any pointers appreciated. :)

2. Sep 17, 2010

$$\frac 1 {1-ut}$$