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To show that an estimator can be consistent with out being

To show that an estimator can be consistent with-out 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, . . ., or n, we use as our estimator the mean of the random sample; otherwise, we use the estimate n2. Show that this estimation procedure is

(a) Consistent;

(b) Neither unbiased nor asymptotically unbiased.

(a) Consistent;

(b) Neither unbiased nor asymptotically unbiased.

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