cdf of $X/(X+Y)$, where $X$ and $Y$ are i.i.d. uniform $X$ and $Y$ are i.i.d. uniform on $[0,1]$. I am asked to find the cdf of $R=\frac{X}{X+Y}$.
I tried to use the auxiliary variable $S=X+Y$, find the joint pdf and then marginalize, but I am not able to find the support of $(R,S)$.
How would you go to do that?


OP wrote:  Find the cdf of $R = \frac{X}{X+Y}$. How would you go to do that?

How would I go to do that? I would use a computer algebra system to do the nitty gritties for me. In this instance, $X$ and $Y$ have joint pdf $f(x,y)$:

(source: tri.org.au)
Then, the cdf of $R = \frac{X}{X+Y}$ is $P(R \le r)$:

(source: tri.org.au)
where Prob is a function from the mathStatica package (I am one of the authors) for Mathematica. All done.
