Conditional moment generating functions

[muso07]

Homework Statement

Random variable U is continuous uniform in the time interval (0,2)
T|U (T given U) is modeled 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)

Homework Equations

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. :)

 

[statdad]

How do you use any mgf to find the mean of the underlying variable? The same method applied to

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

will give E(T | U) (it will be a function of U), and you can also use the conditional mgf to find V(T | U) (another function of U). To find the unconditional expectation and Variance of T, use the notion of double expectation. (E(T) = E(E(T|U)))