(d) Suppose that X(k) is the k-th order statistic where k ~ in (for some T E (0, 1)) and define Dk = X(k) - X(k-1). From lecture, we know that the distribution of n DR is approx- imately Exponential with mean 1/f(F-1(r)). Use this fact to show that the distribution of (n - k + 1)Dk is approximately Exponential with mean 1/h(F-1(r)). (Hint: Note that (i) h(F-1(7)) = f(F-1(7))/(1 -) and (ii) (n - k+1) =n(n- k+1) ~ n(1 -T) since kn ~ T and 1 ~ 0.)