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2. (15 points) {X1,X2,…,Xn} are i.i.d. random variables, E[Xi]=μX, and Var(Xi)=σX2, where i=1,…,n,μX and σX2 ar
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2. (15 points) {X1,X2,…,Xn} are i.i.d. random variables, E[Xi]=μX, and Var(Xi)=σX2, where i=1,…,n,μX and σX2 ar
2. (15 points) {X1,X2,…,Xn} are i.i.d. random variables, E[Xi]=μX, and Var(Xi)=σX2, where i=1,…,n,μX and σX2 are population mean and variance respectively. Consider the following two estimators of population mean, μX. μ^=2X1+XnXˉ=n∑i=1nXi. (a) Is μ^ an unbiased estimator? Is Xˉ an unbiased estimator? Why or why not. (b) Is μ^ a consistent estimator? Is Xˉ a consistent estimator? Why or why not. (c) Which estimator is more efficient? (I.e., which estimator has a smaller variance?)
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