Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 1, pp. 144-154
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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/
@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
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 $n$, $N\to\infty$.
