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THE MULTIPLE SUBSET COUPON COLLECTING PROBLEM

Published online by Cambridge University Press:  08 August 2007

Kuang-Chao Chang  and
Sheldon M. Ross
Kuang-Chao Chang
Affiliation:
Department of Statistics and Information Science Fu Jen Catholic University, Taipei 24205 Taiwan, ROC E-mail: [email protected]
Sheldon M. Ross
Affiliation:
Department of Industrial Engineering and Operations Research University of Southern California Los Angeles, CA 90089 E-mail: [email protected]
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Abstract

Suppose that there are n types of coupons and that each new coupon collected is type i with probability pi. Suppose, further, that there are m subsets of coupon types and that coupons are collected until all of the types of at least one of these subsets have been collected. When these subsets have no overlap, we derive expressions for the mean and variance of the number of coupons that are needed. In the general case where the subsets can overlap, we derive the mean of the number that are needed. We also note that this number is an increasing failure rate on average random variable and we present a conjecture as to a sufficient condition for it to be an increasing failure rate random variable.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 21 , Issue 3 , July 2007 , pp. 435 - 440
Copyright
2007 Cambridge University Press

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