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The coupon-collector's problem revisited

Part of: Combinatorial probability

Published online by Cambridge University Press:  14 July 2016

Ilan Adler ,
Shmuel Oren  and
Sheldon M. Ross
Ilan Adler*
Affiliation:
University of California, Berkeley
Shmuel Oren*
Affiliation:
University of California, Berkeley
Sheldon M. Ross*
Affiliation:
University of California, Berkeley
*
∗ Postal address: Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720, USA.
∗ Postal address: Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720, USA.
∗ Postal address: Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720, USA.
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Abstract

Consider the classical coupon-collector's problem in which items of m distinct types arrive in sequence. An arriving item is installed in system i ≥ 1 if i is the smallest index such that system i does not contain an item of the arrival's type. We study the expected number of items in system j at the moment when system 1 first contains an item of each type

Keywords

Coupon-collector's problemhyperharmonic numbersPoissonization

MSC classification

Primary: 60C05: Combinatorial probability

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 40 , Issue 2 , June 2003 , pp. 513 - 518
Copyright
Copyright © Applied Probability Trust 2003 

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Footnotes

Research supported by the National Science Foundation Grant ECS-0224779 with the University of California.

References

Foata, D., and Zeilberger, D. (2002). The collector's brotherhood problem using the Newman-Shepp symbolic method. To appear in Algebra Univ.Google Scholar
Foata, D., Guo-Niu, H., and Lass, B. (2001). Les nombres hyperharmonique et la fratrie du collectionneur de vignettes. Sem. Lothar. Combinatoire 47, B47a (electronic).Google Scholar
Marshall, A. W., and Olkin, I. (1979). Inequalities: Theory of Majorization and Its Applications (Math. Sci. Eng. 143). Academic Press, New York.Google Scholar
Ross, S. M. (1996). Stochastic Processes, 2nd edn. John Wiley, New York.Google Scholar
Ross, S. M. (2002). Probability Models for Computer Science. Academic Press, New York.Google Scholar