44. Component lifetimes have the exponential distribution with pdf f (x; l)  lelx, x  0, and f (x; l)  0 otherwise, where l 0. However, we wish to estimate the mean m1/l based on the random sample X1, X2, . . . , Xn so let s reexpress the pdf in the form

(1/m)ex/m.

u ~

u ~

 3 1n  12/n4u ˆ

u ˆ

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

b. Use the score function to nd the mle of m.

c. Find the mean and variance of the mle.

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