Question: please provide step by step solution, thanks (a) Let X1, X2, . . . ,Xn denote a simple random sample of size n from a

please provide step by step solution, thanks

(a) Let X1, X2, . . . ,Xn denote a simple random sample of size n from a Normal popu lation with mean it and variance 02. Assuming that n = 2k for some integer k, i.e. n is an even number, one possible estimator of a2 is k A 1 0'2 = 2(X2j X2j_1)2. j=1 (i) Show that 62 is an unbiased estimator for 02. [5 marks] Hint: Explore the behaviour of each term ng X2j_1. - Show that d2 is a consistent estimator for 02. [5 marks]

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