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Question: 1041 to show an estimator can be consistent without being...

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10.41] To show an estimator can be consistent without being unbiased or even asymptotically unbiased, consider the following estimation procedure: To estimate the mean of a population with the finite variance σ2, we first take a random sample of size n. Then, we randomly draw one of n slips of paper numbered from 1 through n, and if the number we draw is 2, 3, ..., orn, we use as our estimator the mean of the random sample; otherwise, we use the estimator n2 Show that this estimation procedure is (a) consistent; and (b)her unbiased nor asymp- totically unbiased.

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