Question: Question 2 [15 marks] Let X1, X2, . . . 1 X. denote a random sample from a population with mean it. and variance 0'2.

Question 2 [15 marks] Let X1, X2, . . . 1 X." denote a random sample from a population with mean it. and variance 0'2. That is. the Xs are independent and each X,- has EX = p. and VUQ) 2 0'2. ISonsider the following three estimators for pa: .. l A 1 X2 -l- . . . -l- X -1 l A #1(X1+X2la \"21X1+W+3Xn1 3X {a} [6 marks] Show that each of the three estimators is unbiased. Show all working. {h} [6 marks] Calculate the variance of each estimator. Show all working. {e} [3 marks] Based on your answers to part [b]. determine whether any of the three estimators is consistent and give an explanation

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