3. In class, I mentioned that the sample has the lowest variance and MSE) of an unbiased estimator of the population. Co

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3 In Class I Mentioned That The Sample Has The Lowest Variance And Mse Of An Unbiased Estimator Of The Population Co 1 (117.91 KiB) Viewed 88 times

3. In class, I mentioned that the sample has the lowest variance and MSE) of an unbiased estimator of the population. Consider once again the example of car ownership and consider a sample of two observations from the population: X, and X2. The sample mean, X, places equal weight on each observation. Therefore, assuming observations are independent, the variance of the sample mean is: i Var(X) =Var(x) ) =ΣΧ =Var(5ΣΧ;) x) =Var(3x: +3x3) =Var(5x1) + Var(3x3) X1 and X, are just random draws from the population so you can plug in your answer to 2(b) or 2(c) to obtain the equivalent variances of X1 and X2. (a) Complete the calculation for the variance of X. (b) Confirm that X is an unbiased estimator of ux. (c) Compute the variance of an alternative estimate of population mean, X*, in which you place a weight of on the first observation and on the second observation. It should have a larger variance since X has the lowest variance. () Compute the variance of an alternative estimate of population mean, X**, in which you place a weight of 1 on the first observation and weight of 0 on the second observation. Again, it should have a larger variance. (e) Compute the variance of a third estimator, X***, in which you place a weight of on the first observation and on the second observation. Confirm that it is smaller than the variance of X. Why is it an unacceptable estimate of ux though?