We have two independent, exponentially distributed random variables X and Y (with parameter a).
Z = X/(X+Y)
What is Z:s distributon function?
The Attempt at a Solution
I think I need some intuition to what I'm really doing with these, I'm having a really tough time and would be extremely grateful for a good explanation.
P(Z < z) = P(X/(X+Y) < z)... Solving this problem corresponds to doing a double integral of f(x,y) over some interval (?) defined by z. Am I getting that correctly? I don't understand how to find that interval. Help??!
Been at this for days but I'm still struggling. Having a hard time finding good materials that cover this aswell...