论文标题
优惠券收藏家的兄弟
The Coupon Collector's Brother
论文作者
论文摘要
收藏家问题的流行变体是：假设有$ n $类型的优惠券具有相同的概率。有一个主要收藏家收集优惠券。当她获得“双人”时，她将其交给了弟弟。因此，当主要收藏家完成她的收藏时，她的哥哥的专辑仍然会有$ u_n $空的空间。我们表明，作为$ n \ to \ infty $，$ u_n/\ ln n $的限制分布指数为$ 1 $。
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 $1$.
