منابع مشابه
Coupon Collecting with Quotas
We analyze a variant of the coupon collector’s problem, in which the probabilities of obtaining coupons and the numbers of coupons in a collection may be non-uniform. We obtain a finite expression for the generating function of the probabilities to complete a collection and show how this generalizes several previous results about the coupon collector’s problem. Also, we provide applications abo...
متن کاملCoupon Collecting
We consider the classical coupon collector’s problem in which each new coupon collected is type i with probability pi; P i1⁄41 n pi1⁄41. We derive some formulas concerning N, the number of coupons needed to have a complete set of at least one of each type, that are computationally useful when n is not too large. We also present efficient simulation procedures for determining P(N . k), as well a...
متن کاملCoupon Collector Problem for Non-Uniform Coupons and Random Quotas
We extend the classical coupon collector problem to find the expected number of selections needed to collect mi (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.
متن کاملCoupon Collecting with or without Replacement, and with Multipurpose Coupons
The classic Coupon-Collector Problem (CCP) is generalized. Only basic probability theory is used. Centerpiece rather is an algorithm that efficiently counts all k-element transversals of a set system.
متن کاملCoupon collecting and transversals of hypergraphs
The classic Coupon-Collector Problem (CCP) is generalized. Only basic probability theory is used. Centerpiece rather is an algorithm that efficiently counts all k-element transversals of a set system.
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2008
ISSN: 1077-8926
DOI: 10.37236/906