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October, 1972 A Note on the Classical Occupancy Problem
C. J. Park
Ann. Math. Statist. 43(5): 1698-1701 (October, 1972). DOI: 10.1214/aoms/1177692405

## Abstract

Assume that $n$ balls are randomly distributed into $N$ equiprobable cells. The ball is presumed to have probability $p, 0 < p < 1$ of staying in the cell and $(1 - p)$ of falling through. Let $S_0$ denote the number of empty cells. In this note we establish the asymptotic normality of $S_0$ as $n$ and $N$ tend to infinity so that $np/N \rightarrow c > 0, np/N^{\frac{5}{6}} \rightarrow \infty$ and $n/N \rightarrow 0$, or $3np/N - \log N \rightarrow - \infty$ and $n/N \rightarrow \infty$. We accomplish this by estimating the factorial cumulants of $S_0$.

## Citation

C. J. Park. "A Note on the Classical Occupancy Problem." Ann. Math. Statist. 43 (5) 1698 - 1701, October, 1972. https://doi.org/10.1214/aoms/1177692405

## Information

Published: October, 1972
First available in Project Euclid: 27 April 2007

zbMATH: 0247.60020
MathSciNet: MR346870
Digital Object Identifier: 10.1214/aoms/1177692405
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