2. City officials are interested in identifying the most dangerous intersections in State College. The city records the number of car accidents at each of n intersections over the course of the year. Let's assume that the number of accidents for a particular intersection i is denoted by Xi . We are provided with a simple random sample of accidents at n intersections, X1, . . . , Xn. Let's assume the following model, Xi i.i.d. Pois() where is an unknown parameter of interest (i.e., the unknown population accident rate).

(a) (3 pts) Show that the MLE of is X. Find its sufficient statistic. Is the MLE a function of the sufficient statistic?

(b) (3 pts) Find the bias, variance, and MSE of MLE.

(c) (3 pts) Does the MLE achieve the Cramer-Rao's lower bound?

(d) (3 pts) Find the asymptotic distribution of the MLE for .

(e) (3 pts) Now, the officials are interested in the total number of accidents expected in those n intersections, that is, E( Pn i=1 Xi) = n. Let us denote this expected total as (= n). Find the MLE of . (Hint: invariance property)

(f) (3 pts) Find the asymptotic distribution of MLE for . (Hint: Delta method)

Please help me solve from a-f

I NEED ONLY TYPING ANSWER