# Determine pdf of function with gamma pdf

1. May 14, 2009

### boneill3

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

Hi Guys,
I have been given the following

The random variable X has a gamma $(\alpha,\beta)$ distribution; ie X has pdf

$f_{X}(x)=\frac{x^{\alpha-1}e^{\frac{-x }{\beta}}} {\Gamma (\alpha)\beta^{\alpha}}\text{for }x \geq 0$

(a) Determine the pdf of:

$Z=\frac{X-\alpha\beta}{\sqrt{\alpha}\beta}.$

DOes anyone know of a good link to explain how to change the pdf like this? I'm not sure where to begin.
Regards
Brendan

2. Relevant equations

3. The attempt at a solution