Use Theorem 11.9 to find the asymptotic distribution of the sample median.

(a) Find the asymptotic distribution for general density f (x).

(b) Find the asymptotic distribution when f (x) »N

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(c) Find the asymptotic distribution when f (x) is double exponential. Write your answer in terms of the variance ¾2 of X.

(d) Compare the answers from

(b) and (c). In which case is the variance of the asymptotic distribution smaller? Do you have an intuitive explanation?