Geodesic
On Calculation of the Power of the Test of Empty Boxes
Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 4, pp. 718-724 
V. P. Čistyakov. On Calculation of the Power of the Test of Empty Boxes. Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 4, pp. 718-724. http://geodesic.mathdoc.fr/item/TVP_1964_9_4_a13/
@article{TVP_1964_9_4_a13,
     author = {V. P. \v{C}istyakov},
     title = {On {Calculation} of the {Power} of the {Test} of {Empty} {Boxes}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {718--724},
     year = {1964},
     volume = {9},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1964_9_4_a13/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let us suppose that $n$ balls are distributed among $N$ boxes, so that each ball may fall into the i-th box with probability $a_i$, $a_i\geqq 0$, $\sum\limits_{i=1}^N a_i=1$, independently of what happens to the other balls. Let $\mu_0$ denote the number of boxes which remain empty. In [5] the proof of the theorem on asymptotic normality of $\mu_0$ under the assumption (1) is not correct. In the present paper a more general theorem on asymptotic normality of $\mu_0$ is proved.