Question: Let X1, X2, X be a random sample from a pdf f(x) that is symmetric about , so that X is an unbiased estimator of

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

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

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

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