I have a density function $f(x,y)= 2e^{-x-y}$ for $0<x<y<\infty$ and $0$ elsewhere. What is the joint distribution function?
So far I have calculated $F(x,y)= \int_0^x \int_0^yf(x',y') dy'dx' = -2e^{-x-y} - 2e^{-x} + 2e^{-y}+2$. However, I'm also assuming that there are two cases, so maybe the $2$nd case would be $\int_0^x \int_0^y f(x',y') dy'dx' + \int_x^y \int_0^x f(x',y') dy'dx'$ ?
Am I on the right track? I would appreciate feedback:)