# PDF of $U = \frac{X}{X + Y}$

Just heads up. This is a homework question, so feel free to prod me towards the answer rather than answering it if you want :)

With two random variables $X~\tilde{}~Exp(1)$ and $Y~\tilde{}~Exp(1)$, I need to find the pdf $~f_U(u)$ of $~U = \frac{X}{X+Y}$.

This question shows that it's a uniform distribution and how to find the mean and variance, but I'm not sure how I'd find the pdf. Would I use the method given on the above page and then work out what the function is given it's uniform (I feel like that's not what the "purpose of the question" is and I may not get full marks)? Or is there another way that I should go about it?

I'm sure there's something super easy I'm missing - I'm not great at statistics and probability stuff - so apologies and thanks in advance :)

• If you know it's uniform, the mean and variance are sufficient to specify the pdf. That's probably the easiest way here. – Paul Oct 3 '16 at 12:43
• The page you link actually shows it's uniform in $(0,1)$, doesn't it? (Both answers do it.) – Clement C. Oct 3 '16 at 12:44