# Math Help - Transformation Technique??

1. ## Transformation Technique??

If X has a uniform density with α=0 and β=1, show that the random variable Y=-2lnX has a gamma distribution. What are its parameters?

2. Originally Posted by Yan
If X has a uniform density with α=0 and β=1, show that the random variable Y=-2lnX has a gamma distribution. What are its parameters?
Here is a start:

The cdf is $F(y) = \Pr(-2 \ln X < y) = \Pr \left( \ln X > - \frac{y}{2} \right) = \Pr \left(X > e^{-y/2} \right) = 1 - \Pr \left(X < e^{-y/2} \right)$ for $0 < y < +\infty$ and zero otherwise.