Geodesic
Asymptotic Normality in a Classical Problem with Balls
Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 2, pp. 223-237 
B. A. Sevast'yanov; V. P. Čistyakov. Asymptotic Normality in a Classical Problem with Balls. Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 2, pp. 223-237. http://geodesic.mathdoc.fr/item/TVP_1964_9_2_a2/
@article{TVP_1964_9_2_a2,
     author = {B. A. Sevast'yanov and V. P. \v{C}istyakov},
     title = {Asymptotic {Normality} in {a~Classical} {Problem} with {Balls}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {223--237},
     year = {1964},
     volume = {9},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1964_9_2_a2/}
}
TY  - JOUR
AU  - B. A. Sevast'yanov
AU  - V. P. Čistyakov
TI  - Asymptotic Normality in a Classical Problem with Balls
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 1964
SP  - 223
EP  - 237
VL  - 9
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TVP_1964_9_2_a2/
LA  - ru
ID  - TVP_1964_9_2_a2
ER  - 
%0 Journal Article
%A B. A. Sevast'yanov
%A V. P. Čistyakov
%T Asymptotic Normality in a Classical Problem with Balls
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1964
%P 223-237
%V 9
%N 2
%U http://geodesic.mathdoc.fr/item/TVP_1964_9_2_a2/
%G ru
%F TVP_1964_9_2_a2

Voir la notice de l'article provenant de la source Math-Net.Ru

Each of $n$ balls is deposited in a cell selected at random out of $N$ given cells.The probability of one cell being selected is equal to ${1/N}$, with the successive selections being mutually independent. Let $0\leqq r_1 be arbitrary fixed integers. The symbol $\mu _r$ denotes a random variable representing the number of those cells that contain exactly $r$ balls. In [3] I. Weiss has proved the integral normal theorem for $\mu_0$ by the method of moments. In this paper we prove the local normal theorem for the random vector $(\mu _{r_1},\dots,\mu _{r_s})$ when $N$, $n\to\infty$ and $0<\alpha _0\leqslant n/{N \leqq\alpha_1}<\infty$ ($\alpha_0$, $\alpha_1$ are constants). In the proof we use the saddle-point method.