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arXiv · 2005.05270

The Coupon Collector's Brother

Vassilis G. Papanicolaou·Aristides V. Doumas
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Abstract

A popular variant of the collector's problem is the following: Assume there are $N$ different types of coupons with equal occurring probabilities. There is one main collector who collects coupons. When she gets a "double," she gives it to her younger brother. Hence, when the main collector completes her collection, her brother's album will still have, say, $U_N$ empty spaces. We show that, as $N \to \infty$, the limiting distribution of $U_N/\ln N$ is exponential with parameter $1$.

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Vassilis G. Papanicolaou, Aristides V. Doumas. 2020-05-11. The Coupon Collector's Brother. https://arxiv.org/abs/2005.05270

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