Let X1,X2,., Xn be independent, discrete random variables, each satisfying P(Xi = k) = 1/N, for k = 1, 2,. Let U and V be random variables defined...

Let X1,X2,..., Xn be independent, discrete random variables, each satisfyingP(Xi = k) = 1/N, for k = 1, 2,... ,N. Let U and V be random variables defined by:U = min {X1,X2,... ,Xn}V = max {X1,X2,... ,Xn}Calculate P(U = k) and P(V = k), for k = 1,2,...,N. (hint: P(U = k) = P(U ≥ k) - P(U ≥ k + 1); also{U ≥ k} = ∩j{Xj ≥ k})