2. Let X1, X2, ..., Xn be iid with Gamma (4, 0), where 0 > 0. n (a) Show that _ Xi is sufficient and complete for 0. (Work required) :=1 (b) Find the MVUE for E (X?) . (Work required) (c Find the MLE for E (X?) . (Work required) (d) Find the Fisher Information based on a single random variable X1. (Work required) (e) Find the MLE for P (X1 > 4). (Work required) (f) Find the asymptotic (limiting) distribution for the MLE in part (e). (Work required) (g) Using the result of (f), construct an approximate (1 - a) 100% confidence interval for P (X1 > 4). (Work required) (h) Given n = 100 and x = 3.838, use (g) to find an approximate 95% confidence interval for P (X1 > 4). (Work required)