X1, X2. .... Xn are iid random variables with mean m and variance o'. M, is the sample mean, i.e., Mn = 2 (a) (8 points) Using the central limit theorem, find an approximate value of P(M, > m+ko) where k is a positive constant. Your answer should be in terms of the standard normal CDF. What is the limiting value of your answer as n tends to infinity? (b) Suppose we know that X1, X2, ..., Xn are iid Bernoulli random variables with an un- known parameter p. Consider the following estimator for the variance of X;: O = Mn(1 - Mn).(i) (6 points) Find the expected value of O. (ii) (2 points) Is O a biased estimator of the variance of X;? (ii) (4 points) Is O a strongly consistent estimator of the variance of X;? Justify your