58. Consider the coupon collecting problem where there are m distinct types of coupons, and each new coupon collected is type j with probability pj , m j=1 pj = 1. Suppose you stop collecting when you have a complete set of at least one of each type. Show that P{i is the last type collected} = E

.

j=i

(1 − Uλj /λi)

/

where U is a uniform (0, 1) random variable.