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COUPON COLLECTING

Published online by Cambridge University Press:  19 March 2008

Mark Brown ,
Erol A. Peköz  and
Sheldon M. Ross
Mark Brown
Affiliation:
Department of MathematicsCity CollegeCUNY New York, NY E-mail: [email protected]
Erol A. Peköz
Affiliation:
Department of Operations and Technology ManagementBoston UniversityBoston, MA 02215 E-mail: [email protected]
Sheldon M. Ross
Affiliation:
Department of Industrial and System EngineeringUniversity of Southern CaliforniaLos Angeles, CA 90089 E-mail: [email protected]
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Abstract

We consider the classical coupon collector's problem in which each new coupon collected is type i with probability pi; ∑i=1npi=1. 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 as analytic bounds for this probability.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 22 , Issue 2 , March 2008 , pp. 221 - 229
Copyright
Copyright © Cambridge University Press 2008

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References

1.Adler, I., Oren, S., & Ross, S.M. (2003). The coupon-collector's problem revisited. Journal of Applied Probability. 40 (2): 513–518.CrossRefGoogle Scholar
2.Diaconis, P. & Fill, J.A. (1990). Strong stationary times via a new form of duality. Annals of Probability 18 (4): 1483–1522.CrossRefGoogle Scholar
3.Ross, S. & Peköz, E.A. (2007). A second course in probability (probabilitybookstore.com.)Google Scholar