Question

There are k types of coupons. independently of the types of previously collected coupons, each new coupon collected is of type i with probability pi, ki =1 pi = 1. if n coupons are collected, find the expected number of distinct types that appear in this set. (that is, find the expected number of types of coupons that appear at least once in the set of n coupons.)

Answer 1

Let X be the expected number of distinct types of coupons in the collection of k coupons X = X1 + X2 + ……. + Xx.