Please provide clear, detailed, and neat solutions step by step? Thank You!

6. Let X1, X2, . .. be a random sample of independent, identically distributed variables with Xi ~ Ber(0), where 0 E (0, 1). Suppose we are interested in parametric estimators of Var(Xi) = g(0) = 0(1 - 0). Let Xn be the sample mean of the random sample. (a) Find E[Xn]. Is Xn an unbiased estimator of 0 ? (b) Find E[Xn(1 - Xn)]. Is Xn(1 - Xn) an unbiased estimator of g(0) ? (c) Find an unbiased estimator of g(0) = 0(1 -0) (d) Find a consistent estimator for g(0) = 0(1 - 0) (e) Suppose 0 # 5, Find the asymptotic distribution of n[X,(1 - Xn) - 0(1 - 0)] . (Hint: Use the delta theorem)