A set of random variables, X1, X2, X3, Xn, are independent and each uniformly distributed over ( 0, 1).
(a) Find the probability density function of Z = max(X1, X2… Xn).
(b) With defined as in part (a) above, let A be the event {X1 = 1/ 2} and find fZ|A (z). That is, find the conditional PDF of Z given {X1 = 1/ 2}