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 m If n is large, it can be shown that V(), 1 (4n f () 2) a Compare V() to V() when the underling distribution is normal b When the underlying pdf is Cauchy (see Example 6 7), V() , ...

Let X1, X2, ... , Xn be a random sample from a pdf f (x) that is

Question:

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 m. If n is large, it can be shown that V(), ≈ 1/(4n[ f (µ)]2).
a. Compare V() to V() when the underling 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?
Distribution
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