Coupon Collecting with or without Replacement, and with Multipurpose Coupons
نویسنده
چکیده
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.
منابع مشابه
Coupons 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 کاملThe Coupon Subset Collection Problem
The coupon subset collection problem is a generalization of the classical coupon collecting problem, in that rather than collecting individual coupons we obtain, at each time point, a random subset of coupons. The problem of interest is to determine the expected number of subsets needed until each coupon is contained in at least one of these subsets. We provide bounds on this number, give effic...
متن کاملCoupon 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 کاملOptimal strategy of coupon subset collection when each package contains half of the coupons
The coupon subset collection is a generalization of the classical coupon collection, where instead of selecting (with replacement) a single coupon, a subset of at most k coupons (known as a “package”) is selected in each round. In this paper, we study how to design the collection of packages and assign probabilities to the packages, so as to minimize the expected number of rounds to collect all...
متن کاملThe Generalised Coupon Collector Problem
Coupons are collected one at a time from a population containing n distinct types of coupon. The process is repeated until all n coupons have been collected and the total number of draws, Y , from the population is recorded. It is assumed that the draws from the population are independent and identically distributed (draws with replacement) according to a probability distributionXwith the proba...
متن کامل