The Coupon Collector's Brother

2020/05/11 by Papanicolaou, Vassilis G., Doumas, Aristides V.
#60F05 #60F99 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2005.05270

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 → ∞, the limiting distribution of U_N/ln N is exponential with parameter 1.

Related

• The Siblings of the Coupon Collector
• Limit theorems in the extended coupon collector's problem
• Approximation Theorems Related to the Coupon Collector's Problem
• The number of k-tons in the coupon collector problem
• Some new aspects of the coupon-collector's problem