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Limit distributions for the problem of collecting pairs

14 May 2008
Pavle Mladenović
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Abstract

Let Nn={1,2,...,n}N_n=\{1,2,...,n\}Nn​={1,2,...,n}. Elements are drawn from the set NnN_nNn​ with replacement, assuming that each element has probability 1/n1/n1/n of being drawn. We determine the limiting distributions for the waiting time until the given portion of pairs jjjjjj, j∈Nnj\in N_nj∈Nn​, is sampled. Exact distributions of some related random variables and their characteristics are also obtained.

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