42. Assume that the number of defects in a car has a Poisson distribution with parameter l. To estimate l we obtain the random sample X1, X2, . . . , Xn.

a. Find the Fisher information in a single observation using two methods.

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

c. Use the score function to nd the mle of l and show that the mle is an ef cient estimator.

d. Is the asymptotic distribution of the mle in accord with the second theorem? Explain.