Question: Question 2 (20 points) Let X, X,,.., X be iid observations from a Bernoulli( p) distribution, the pdf of X is given by f(x; p)

Question 2 (20 points) Let X, X,,.., X be iid observations from a Bernoulli( p) distribution, the pdf of X is given by f(x; p) = p*(1- p)" * for xe {0, 1) a) Use the moment-generating function (mgf) of X to find the distribution of T = > X, (6 points) (hint: you may use the mgf of Bernoulli distribution Mx(t) = (q + pet), where q = 1 - p) b) Show that 7 is sufficient p(show the steps to get full credicts). (8 points) c) It is easy to know 7 is complete for p, find the UMVUE of p.(6 points)

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