50.

a. Let X1, . . . , Xn be a random sample from a uniform distribution on [0, u]. Then the mle of u is

Y  max(Xi). Use the fact that Y y iff each Xi y to derive the cdf of Y. Then show that the pdf of Y  max(Xi) is

b. Use the result of part

(a) to show that the mle is biased but that (n  1)max(Xi)/n is unbiased.