=+14.1. Let X1,...,Xn be an i.i.d. sample from a distribution with cdf F and pdf

f, and X(1) < ··· < X(n) be the order statistics. Then the cdf of X(i)

is given by G(i)(x) = n k=i

n k



{F(x)}k{1 − F(x)}n−k, and the pdf of Xi is given by g(i)(x) = n!

(i − 1)!(n − i)!{F(x)}i−1{1 − F(x)}n−i f(x).

Using these results, derive the cdf and pdf of R in Example 14.2, assuming n = 2m − 1 for simplicity.

518 14 Jackknife and Bootstrap