Coupon Collector Problem for Non-Uniform Coupons and Random Quotas

Abstract

We extend the classical coupon collector problem to find the expected number of selections needed to collect $m_i$ (possible random) copies of coupon $i$, when the distribution of the coupons is not necessarily equally likely.  Upper and lower bounds which provide limiting asymptotics are also obtained for the expected number of selections needed to fulfill a random quota for each coupon.