Question: please try solve it! Problem 4 (unbiased, efficient, and consistent estimators). Suppose we have n i.i.d. samples distributed according to N(u, 02). Consider two estimators

please try solve it!

Problem 4 (unbiased, efficient, and consistent estimators). Suppose we have n i.i.d. samples distributed according to N(u, 02). Consider two estimators for u: X = LEL, Xi and X = }(X1 + Xn). A) Calculate the mean of X and X. Are they unbiased? B) Calculate the variance of X and X. Which one is more efficient? C) If n - oo, X and X will converge to what? which one is the consistent estimator

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