Take themodel f (x) exp(x),x 0, 0. (a) Find the Cramr-Rao lower bound

Take themodel f (x) Æ µ exp(¡µx),x ¸ 0,µ È 0.

(a) Find the Cramér-Rao lower bound for µ.

(b) Recall the MLE bµ for µ from above. Notice that this is a function of the sample mean. Use this formula and the delta method to find the asymptotic distribution for bµ.

(c) Find the asymptotic distribution for bµ using the general formula for the asymptotic distribution of MLE. Do you find the same answer as in part (b)?