Finding distribution functions of exponential random variables Find the distribution functions of X+Y/X and X+Y/Z, given that X, Y, and Z have a common exponential distribution.
I think the main thing is that I wanted to confirm the distribution I got for X+Y. I'm doing the integral, and my calculus is a little rusty. I'm getting -e^-ax - ae^-as with parameters x from -infinity to infinity.
From there presumably I can just treat X+Y like one variable and then divide by z.
Thanks so much!

Thanks so much for your help. I'm still having some trouble, however. Currently for (X+Y)/X I have denoted X+Y = t, adn the distribution of T is \int \boldsymbol{\alpha e^{-\alpha x}(1+\alpha x + \frac{(\alpha x)^2}{2})}. Then doing the integral caculations for the distribution, I get \int \boldsymbol{\alpha e^{-\alpha t x}(1+\alpha t x + \frac{(\alpha t x)^2}{2})}. This seems right but for some reason I'm not getting the answer I'm supposed to. Is it because X+Y and X are related? Would this work for (X+Y)/Z?
Thanks!
