Given f(x) = e^-x and f(y|x) = 1/x e^(-y/x). Three parts: (a) Compute density of (x,y), (b) Compute E(y) and (c) Compute P(y>x).
f(x,y) = f(y|x)f(x)
if f(x) = ve^(-vx), then E(x)=v^(-1)
The Attempt at a Solution
I'm stuck on a problem. I was given f(x) and f(y|x) and was able to derive f(x,y) and compute E(y). The third step of the problem is computing P[y>x]. I think I need to know f(y) to answer this problem but I can't figure out how to derive it. Or is there a way to compute P(y>x) given the info I know without deriving f(y)?