# Integration of probability distributions

1. Oct 6, 2009

### cse63146

1. The problem statement, all variables and given/known data

http://img24.imageshack.us/img24/8093/asss4.jpg [Broken]

2. Relevant equations

3. The attempt at a solution

So I got this far:

$$\frac{\Gamma(\alpha + k)}{\Gamma(h) \Gamma(\alpha) \Gamma(k)} \int^{\infty}_0 \int^{\infty}_0 \frac{e^{-(h^{-1} + \lambda) \theta}\theta^{k+x-1} \lambda^{k+x-1} h^{-2k}}{(1+h^{-1} \lambda)^{\alpha + k}}d \lambda d \theta$$

Do I have to use integration by parts to integrate lambda out?

Last edited by a moderator: May 4, 2017