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Problem 4 Suppose (Y1, ..., Yn) are i.i.d. and P[Yi] = my, V[Yi] = of. Suppose n is even and consider the following estimator of

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Problem 4 Suppose (Y1, ..., Yn) are i.i.d. and P[Yi] = my, V[Yi] = of. Suppose n is even and consider the following estimator of the population mean n /2 n 1 Yn 3 Yit Yi 2n 2n i=n/2+1 1. Find E Yn . Is Yn an unbiased estimator of the population mean My? 2. Find V Yn . 3. Is Yn a better estimator than the sample average Yn = ? > Y? Why

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