Question 4.26 ,Page 195. Statistical inference, Second Edition, George Casella, Roger L.Berger.

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

Z=min{X,Y} and W={1 if Z=X and 0 if Z=Y}

(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(Hint: Show that P(Z<=z|W=i)=P(Z<=z) for i=0 or 1.)

I need detailed solution please.