Question: Let X1, X2, X3 and X4 be a random sample of size n = 4 drawn from a N (y; (72) distribution. Consider the following

Let X1, X2, X3 and X4 be a random sample of size n = 4 drawn from a N (y; (72) distribution. Consider the following two estimators of the population mean 14. _&+&+&+& T1 4 (The sample mean) = 2X1+X2+X3+2X4 T2 6 (A weighted mean) (a) Show that both T1 and T2 are unbiased estimators of y. (5) (b) Compute Var(T1) and Var(T2) (5) (c) Suppose X1 = .95,X2 = .85,X3 = .92 and X4 = 1.00, Construct a 95% condence inter- val for the population mean y from the estimators T1 and T2

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