* 16. Let X1, X2, . . . be independent random variables each having distribution function F and density function f . The order statistics X(1), X(2), . . . , X(n) of the subsequence X1, X2, . . . , Xn are obtained by rearranging the values of the Xi in non-decreasing order. That is to say, X(1) is set to the smallest observed value of the Xi , X(2) is set to the second smallest value, and so on, so that X(n) = max{X1, X2, . . . , Xn}. The sample median Yn of the sequence X1, X2, . . . , Xn is the ‘middle value’, so that Yn is defined to be Yn =

(

X(r+1) if n = 2r + 1 is odd, 1 2 (X(r) + X(r+1)) if n = 2r is even.