5. (Rao-Blackwell theorem) Let X1, X2, ..., Xn be independent Bernoulli random vari- ables with an unknown probability of success p. Denote S = X1 + X2+ . . . + Xn. a) Prove that S is a sufficient statistic for the estimation of parameter p. b) Find the conditional pmf f(x|s) = P(X1 = x|S = s) of X1 given S = s. c) Find the conditional expectation E(X1 |S = s). d) Explain the meaning of the result you obtained in Part c) in the light of the Rao-Blackwell theorem