# Ratio of two beta random variables

I'm working on a problem for an hour and I wanted to get some hints. Suppose:

$y_1, y_2, y_3, y_4 \sim Dir(\alpha_1, \alpha_2, \alpha_3, \alpha_4)$

what is the distribution of $\frac{y_1}{y_1 + y_2}$ ?

My guess is that distribution should be $Beta(\alpha_1, \alpha_2)$

Could you guys give me some hints on how to show it?

• What is the beta distribution specified by four parameters? – Mankind May 7 '15 at 17:26
• @HowDoIMath, my bad! it's dirichlet. – Linda May 7 '15 at 17:35