Let X1, X2, ... , Xn denote a random sample from b(1, p). We know that X is an unbiased estimator of p and that Var( X ) = p(1 p)/n. (See Exercise 6.4-12.) (a) Find the RaoCramr lower bound for the variance of every unbiased estimator of p. (b) What is the efficiency of X as an estimator of p?

ST 701 Week 8 Notes and Week 9 Notes MaLyn Lawhorn October 3, 2017, October 10, 2017, and October 12, 2017 Alternative Generating Functions There are some other generating functions besides MGFs. itx p ▯ Characteristic Functiox: ’ (t) = ], i =▯1 ▯ eitis bounded ▯ Probability Generating Function: P (t) = E[t ] (assume existence) X Back to Normal Distribution We know that X = ▯ + ▯Z and X ▯ ▯ ▯ = Z: Additionally, the CDF of X is ▯ ▯ ▯ ▯ X ▯ ▯