## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 43, Number 5 (1972), 1698-1701.

### A Note on the Classical Occupancy Problem

#### 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 $S_0$.

#### Article information

**Source**

Ann. Math. Statist., Volume 43, Number 5 (1972), 1698-1701.

**Dates**

First available in Project Euclid: 27 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177692405

**Digital Object Identifier**

doi:10.1214/aoms/1177692405

**Mathematical Reviews number (MathSciNet)**

MR346870

**Zentralblatt MATH identifier**

0247.60020

**JSTOR**

links.jstor.org

#### Citation

Park, C. J. A Note on the Classical Occupancy Problem. Ann. Math. Statist. 43 (1972), no. 5, 1698--1701. doi:10.1214/aoms/1177692405. https://projecteuclid.org/euclid.aoms/1177692405