# Transformation of two gamma variables

If you have $\frac{X}{X+Y}$ where X and Y are both independent Gamma distributions where $\alpha$ for both X and Y is different, but $\beta$ is the same for both, then how would that be different from the pdf for $\frac{X}{X+Y}$ where alpha is the same but beta is different?

The first scenario is given at the top of this pdf http://www.math.wm.edu/~leemis/chart/UDR/PDFs/GammaBeta.pdf

• won't be answerable only from knowledge of the marginal distributions; you need to know the joint distribution. – Glen_b Oct 26 '16 at 11:26
• Sorry I forgot to mention that these are independent variables and therefore the joint distribution is easily obtainable. – gorge Oct 26 '16 at 11:43
• Please make sure that information needed to answer the question is made clear in the question. i.e. please edit your question – Glen_b Oct 26 '16 at 20:28
• Is this the solution? math.stackexchange.com/a/190695 – gorge Oct 27 '16 at 6:37
• Yes, it is! ..... – kjetil b halvorsen Oct 1 '17 at 15:10