X,Y are independent exponentially distributed then what is the distribution of X/(X+Y) Been crushing my head with this exercise. I know how to get the distribution of a ratio of exponential variables and of the sum of them, but i can't piece everything together.
The exercise goes as this:
If X,Y are independent exponentially distributed with beta = 1 (parameter of the exponential distribution = 1) then what is the distribution of X/(X+Y)
Any ideas?
Thanks a lot.

In other words, for each $a > 0$, you want to compute $P\left(\frac{X}{X+Y} < a \right)$.
Outline: Find the joint density of $(X,Y)$, and integrate it over the subset of the plane $\left\{ (x,y) : \frac{x}{x+y} < a \right\}$.
