2. (15 points) {X₁, X2,..., Xn} are i.i.d. random variables, E[X₂] = x, and Var (X₂) = o, where i = 1,...,n, ux and ok a

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2 15 Points X X2 Xn Are I I D Random Variables E X X And Var X O Where I 1 N Ux And Ok A 1 (35.21 KiB) Viewed 29 times

2. (15 points) {X₁, X2,..., Xn} are i.i.d. random variables, E[X₂] = x, and Var (X₂) = o, where i = 1,...,n, ux and ok are population mean and variance respectively. Consider the following two estimators of population mean, px. X₁ + Xn 2 (a) Is û an unbiased estimator? Is X an unbiased estimator? Why or why not. (b) Is û a consistent estimator? Is X a consistent estimator? Why or why not. (c) Which estimator is more efficient? (I.e., which estimator has a smaller variance?) = X Σi=1 Xi n =