Question: Let X1, X2, . . . , Xn be a random sample from a pdf f(x) that is symmetric about m, so that is an

Let X1, X2, . . . , Xn be a random sample from a pdf f(x) that is symmetric about m, so that is an unbiased estimator of

. If n is large, it can be shown that V( ) 1/(4n[ f(m)]2

).

a. Compare V( ) to V( ) when the underlying distribution is normal.

b. When the underlying pdf is Cauchy (see Example 6.7), V( ) , so is a terrible estimator. What is V( ) in this case when n is large?

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