2.21 Let X(1)

(a) Show that X(r) and X(s)X(r) are independent for any s>r.

(b) Find the distribution of X(rþ1)X(r).

(c) Show that E(X(i)) ¼

Pij

¼1 1=(n þ 1  j).

(d) Interpret the significance of these results if the sample arose from a life test on n light bulbs with exponential lifetimes.