标题： 收集对问题的极限分布 显示英文标题

标题： Limit distributions for the problem of collecting pairs

摘要： 设 $N_n=\{1,2,...,n\}$。 元素从集合 $N_n$中有放回地抽取，假设每个元素被抽取的概率为 $1/n$。 我们确定了在给定的对 $jj$, $j\in N_n$被抽样之前的等待时间的极限分布。 一些相关随机变量的精确分布及其特征也得到了。 显示英文摘要

摘要： Let $N_n=\{1,2,...,n\}$. Elements are drawn from the set $N_n$ with replacement, assuming that each element has probability $1/n$ of being drawn. We determine the limiting distributions for the waiting time until the given portion of pairs $jj$, $j\in N_n$, is sampled. Exact distributions of some related random variables and their characteristics are also obtained.