# Simulating the Coupon Collector Problem

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A statement of the coupon collector problem: suppose each box of cereal contains a coupon chosen at random from possible coupons. Let be the number of boxes of cereal that need to be purchased in order to get a complete set of all coupons. What is the expected value (or waiting time) of ? The answer is given by the formula .

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Contributed by: Yikai Teng (May 2019)

Based on an undergraduate research project at the Illinois Geometry Lab by Raymond Harpster, Tianli Li, Yikai Teng and directed by A. J. Hildebrand.

Open content licensed under CC BY-NC-SA

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Reference

[1] B. Dawkins, "Siobhan's Problem: The Coupon Collector Revisited," *The American Statistician*, 45(1), 1991 pp. 76–82. doi:10.1080/00031305.1991.10475772.

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