# Generating Random Variables

• November 13th 2006, 11:36 AM
WeeG
Generating Random Variables
hello people, I need some help with computational statistics:

I need to proof that :

if X~(a,t) and Y~(b,t) then X / ( X+Y) ~Beta(a,b)

( hint: I think I need to use the inverse transform method )

thanks !!!
• November 16th 2006, 08:02 AM
CaptainBlack
Quote:

Originally Posted by WeeG
hello people, I need some help with computational statistics:

I need to proof that :

if X~(a,t) and Y~(b,t) then X / ( X+Y) ~Beta(a,b)

( hint: I think I need to use the inverse transform method )

thanks !!!

Should be:

if $X\sim \Gamma(a,t)$ and $Y\sim \Gamma(b,t)$ then $X / ( X+Y) \sim \mbox{Beta}(a,b)$

See here section with equations 33-42.

RonL