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A Survey of the Coupon Collector’s Problem with Random Sample Sizes

John E. Kobza (), Sheldon H. Jacobson () and Diane E. Vaughan ()
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John E. Kobza: Texas Tech University
Sheldon H. Jacobson: University of Illinois
Diane E. Vaughan: Los Alamos National Laboratory

Methodology and Computing in Applied Probability, 2007, vol. 9, issue 4, 573-584

Abstract: Abstract This paper surveys the coupon collector’s waiting time problem with random sample sizes and equally likely balls. Consider an urn containing m red balls. For each draw, a random number of balls are removed from the urn. The group of removed balls is painted white and returned to the urn. Several approaches to addressing this problem are discussed, including a Markov chain approach to compute the distribution and expected value of the number of draws required for the urn to contain j white balls given that it currently contains i white balls. As a special case, E[N], the expected number of draws until all the balls are white given that all are currently red is also obtained.

Keywords: Coupon collector’s problem; Markov chain; Transient analysis; Waiting times; Primary 65C40 Computational Markov chains; Secondary 60C05 Combinatorial probability (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s11009-006-9013-3

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