43. In Example 7.23 f (x; u)  1/u for 0 x

u and 0 otherwise. Given a random sample, the maximum likelihood estimate is the largest observation.

a. Letting , show that is unbiased and nd its variance.

b. Find the Cram r—Rao lower bound for the variance of an unbiased estimator of u.

c. Compare the answers in parts

(a) and

(b) and explain why it is apparent that they disagree. What assumption is violated, causing the theorem not to apply here?