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Teoriya Veroyatnostei i ee Primeneniya, 1967, Volume 12, Issue 1, Pages 144–154
(Mi tvp695)
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This article is cited in 10 scientific papers (total in 10 papers)
Short Communications
Convergence of the Distribution of the Number of Empty Boxes to Gaussian and Poisson Processes in a Classical Problems with Balls
B. A. Sevast'yanov Moscow
Abstract:
Let $n$ balls be dropped at random into $N$ boxes. Each ball may fall into any box with the same probability $1/N$, independently of what, happens to the other balls. Let $\mu_0(n)$ be the number of empty boxes. We consider $\mu_0(n)$ as a random function of time parameter $n$. We prove that the distribution of random function $\mu_0(n)$ converges to the distribution of a Gaussian or Poisson process as $n$, $N\to\infty$.
Received: 25.01.1966
Citation:
B. A. Sevast'yanov, “Convergence of the Distribution of the Number of Empty Boxes to Gaussian and Poisson Processes in a Classical Problems with Balls”, Teor. Veroyatnost. i Primenen., 12:1 (1967), 144–154; Theory Probab. Appl., 12:1 (1967), 126–134
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