X and Y are independent random variables with X ~ exponential(λ) and Y ~ exponential(μ). It is impossible to obtain direct observations of X and Y. Instead, we observe the random variables Z and W, where

(This is a situation that arises, in particular, in medical experiments. The X and Y variables are censored.)
(a) Find the joint distribution of Z and W.
(b) Prove that Z and W are independent. (Show that P(Z

Z-min(X,Y) and w z-x