Let X and Y be independent and identically distributed (i.i.d.) r.v.’s, each having the probability distribution, p(k) = (1 − λ)λ^k; k = 0,1..... where λ :(0; 1) is a constant. Define U = min(X; Y ); V = max(X; Y ); W = V − U. Determine the joint probability distribution of U and W (taking care with W = 0) and verify that U and W are independent r.v.’s.