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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
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

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