Convergence of the Distribution of the Number of Empty Boxes to Gaussian and Poisson Processes in a Classical Problems with Balls
Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 1, pp. 144-154
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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 $n$, $N\to\infty$.
@article{TVP_1967_12_1_a15,
author = {B. A. Sevast'yanov},
title = {Convergence of the {Distribution} of the {Number} of {Empty} {Boxes} to {Gaussian} and {Poisson} {Processes} in {a~Classical} {Problems} with {Balls}},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {144--154},
year = {1967},
volume = {12},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1967_12_1_a15/}
}
TY - JOUR AU - B. A. Sevast'yanov TI - Convergence of the Distribution of the Number of Empty Boxes to Gaussian and Poisson Processes in a Classical Problems with Balls JO - Teoriâ veroâtnostej i ee primeneniâ PY - 1967 SP - 144 EP - 154 VL - 12 IS - 1 UR - http://geodesic.mathdoc.fr/item/TVP_1967_12_1_a15/ LA - ru ID - TVP_1967_12_1_a15 ER -
%0 Journal Article %A B. A. Sevast'yanov %T Convergence of the Distribution of the Number of Empty Boxes to Gaussian and Poisson Processes in a Classical Problems with Balls %J Teoriâ veroâtnostej i ee primeneniâ %D 1967 %P 144-154 %V 12 %N 1 %U http://geodesic.mathdoc.fr/item/TVP_1967_12_1_a15/ %G ru %F TVP_1967_12_1_a15
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. Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 1, pp. 144-154. http://geodesic.mathdoc.fr/item/TVP_1967_12_1_a15/