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Teoriya Veroyatnostei i ee Primeneniya, 1968, Volume 13, Issue 1, Pages 39–50
(Mi tvp791)
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This article is cited in 3 scientific papers (total in 3 papers)
Convergence of the variables $\mu_r(n)$ to Gaussian and Poisson processes in the classical problem with balls
Yu. V. Bolotnikov Moscow
Abstract:
Let $n$ balls be distributed at random in $N$ boxes. Each ball may fall into any box with the same probability $1/N$ independently of the others. Let $\mu_r(n)$ be the number of boxes which contain exactly $r$ balls $(r=1,2,\dots)$. We consider $\mu_r(n)$ as a random function of the time parameter $n$. In this paper we prove that the random function $\mu_r(n)$ converges to some Gaussian or Poisson process as $n$, $N\to\infty$.
Received: 19.12.1966
Citation:
Yu. V. Bolotnikov, “Convergence of the variables $\mu_r(n)$ to Gaussian and Poisson processes in the classical problem with balls”, Teor. Veroyatnost. i Primenen., 13:1 (1968), 39–50; Theory Probab. Appl., 13:1 (1968), 39–51
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https://www.mathnet.ru/eng/tvp791 https://www.mathnet.ru/eng/tvp/v13/i1/p39
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Abstract page: | 146 | Full-text PDF : | 98 |
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