Teoriâ veroâtnostej i ee primeneniâ, Tome 13 (1968) no. 1, pp. 39-50
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Yu. V. Bolotnikov. Convergence of the variables $\mu_r(n)$ to Gaussian and Poisson processes in the classical problem with balls. Teoriâ veroâtnostej i ee primeneniâ, Tome 13 (1968) no. 1, pp. 39-50. http://geodesic.mathdoc.fr/item/TVP_1968_13_1_a2/
@article{TVP_1968_13_1_a2,
author = {Yu. V. Bolotnikov},
title = {Convergence of the variables $\mu_r(n)$ to {Gaussian} and {Poisson} processes in the classical problem with balls},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {39--50},
year = {1968},
volume = {13},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1968_13_1_a2/}
}
TY - JOUR
AU - Yu. V. Bolotnikov
TI - Convergence of the variables $\mu_r(n)$ to Gaussian and Poisson processes in the classical problem with balls
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1968
SP - 39
EP - 50
VL - 13
IS - 1
UR - http://geodesic.mathdoc.fr/item/TVP_1968_13_1_a2/
LA - ru
ID - TVP_1968_13_1_a2
ER -
%0 Journal Article
%A Yu. V. Bolotnikov
%T Convergence of the variables $\mu_r(n)$ to Gaussian and Poisson processes in the classical problem with balls
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1968
%P 39-50
%V 13
%N 1
%U http://geodesic.mathdoc.fr/item/TVP_1968_13_1_a2/
%G ru
%F TVP_1968_13_1_a2
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 $n$, $N\to\infty$.
