The Hypergeometric Coupon Collection Problem and its Dual
author
Abstract:
Suppose an urn contains M balls, of different types, which are removed from the urn in a uniform random manner. In the hypergeometric coupon collection problem, we are interested in the set of balls that have been removed at the moment when at least one ball of each type has been removed. In its dual, we are interested in the set of removed balls at the first moment that this set contains all of the balls of at least one type.
similar resources
The 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...
full textEn passant Coupon Collection
Spontaneous interaction in public places has evolved as crucial concern in interaction design, particularly in the domain of public advertising. Implicit interaction is a mode of spontaneous interaction in which the user is not attentively or explicitly expressing input to a system, but the system from observing the user, and considering all the available information that describes the user sit...
full textThe Coupon Collector’s Problem
In this note we will consider the following problem: how many coupons we have to purchase (on average) to complete a collection. This problem, which takes everybody back to his childhood when this was really “a problem”, has been considered by the probabilists since the eighteenth century and nowadays it is still possible to derive some new results, probably original or at least never published...
full textGeneralized Coupon Collection: the Superlinear Case
We consider a generalized form of the coupon collection problem in which a random number, S, of balls is drawn at each stage from an urn initially containing n white balls (coupons). Each white ball drawn is colored red and returned to the urn; red balls drawn are simply returned to the urn. The question considered is then: how many white balls (uncollected coupons) remain in the urn after the ...
full textDeterministic Coupon Collection and Better Strong Dispersers
Hashing is one of the main techniques in data processing and algorithm design for very large data sets. While random hash functions satisfy most desirable properties, it is often too expensive to store a fully random hash function. Motivated by this, much attention has been given to designing small families of hash functions suitable for various applications. In this work, we study the question...
full textThe Coupon-Collector Problem Revisited
A standard combinatorial problem calls to cstlmate the expected number of purchases of coupons needed LO complete Ute collection of all possible m different types. Generalizing this problem. by letting lhe coupons be obtained with an arbitrary probability distribution. and considering other related processes, the problem has been found to model many practical siwations. The usefulness of lhis m...
full textMy Resources
Journal title
volume 1 issue 1
pages 1- 7
publication date 2007-04-01
By following a journal you will be notified via email when a new issue of this journal is published.
Keywords
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023