Question: 18. Let X1, X2, . . . , Xn be a random sample from a pdf f(x) that is symmetric about , so that is

18. Let X1, X2, . . . , Xn be a random sample from a pdf f(x) that is symmetric about , so that is an unbiased estimator of . If n is large, it can be shown that V( ) 1/(4n[ f( )]2

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

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

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