I would be happy enough to just get help with c), if parts a) and b) are too difficult.

Thanks in advance!

X~ Q2. If a random variable, X, has a geometric distribution with parameter p E (0,1), we write Geometric(p) and the probability mass function of X is P(1 p)2-1 & {1, 2, 3, ...}; P(X = x) otherwise. 73-** and E(X) = 1 Suppose that X1,..., Xn are independent and identically distributed random variables, where Xi Geometric(p) for i E {1,..., n}. The following estimator, , is proposed as an estimator for p if X1 = 1; --{ 0 otherwise. (a) Use the Rao-Blackwell theorem to find an unbiased estimator of p, denoting this esti- mator, such that Var()