46. Let X1, X2, . . . , Xn be a random sample from the normal distribution with known mean m but with the variance s2 as the unknown parameter.

a. Find the information in a single observation and the Cram r—Rao lower bound.

b. Find the mle of s2.

c. Find the distribution of the mle.

d. Is the mle an ef cient estimator? Explain.

e. Is the answer to part

(c) in con ict with the asymptotic distribution of the mle given by the second theorem? Explain.