successfully proven Let X = (X1, X2, ..., Xn) be a random sample of size n from the density f(x; 0) = 0(1 - 0), x= {0, 1, 2, .. . }, Here 0 E (0, 1) is an unknown parameter. The mean and variance of X are given respectively by E(X) = 1 - 0 and Var(X) -1 - 0 02 a Use any argument to prove that T = _ _, Xi is a complete and minimal suffi- cient statistic for 0. b) Show and argue that the expected Fisher information about 0 contained in the statistic found in a) is n IT(0) = 02 ( 1 - 0 ) c) Derive the UMVUE of h(0) = 0. Simply your UMVUE as much as possible. Hint: Use the interpretation that P(X1 = 0) = 0 and the fact that T = Xi ~ Negative Binomial(n, 0) i= 1 with probability mass function P(T = t) = (n+t- 1) on(1 -0)*, t = 0, 1,2