Suppose U1, U2, ..., Un are independent random variables and for every i = 1, ..., n, Ui has a uniform distribution over [0, 1].
(a) Find the probability density function of M = max(U1, ..., Un). (We solved the case n = 2 in class. This a generalization.)
(b) Define Z = min(U1, ..., Un). Find the c.d.f. and the p.d.f of Z. (Hint: write the event {Z > z} in terms of random variables U1, ..., Un.)