Question: Question 2: Let \({{X}_{1}},...,{{X}_{n}}\) be i.i.d. observations from an exponential ( \(\lambda \) ) distribution, the p.d.f. of X is given by

a) Use the moment-generating function of X to find the distribution of (10 points)

b) Show that T is sufficient for \(\lambda \). (8 points)

c) It is easy to show that T is also complete for \(\lambda \). Find the UMVUE of (6 points)