On Calculation of the Power of the Test of Empty Boxes

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.