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A restricted occupancy problem

Published online by Cambridge University Press:  14 July 2016

Kai-Tai Fang
Kai-Tai Fang*
Affiliation:
Institute of Applied Mathematics, Academia Sinica
*
∗The author is Associate Professor, Institute of Applied Mathematics, Academia Sinica, Beijing, China. This work was done in the Department of Epidemiology and Public Health, Yale University.
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Abstract

There are m urns each containing k cells; n balls are assigned to the m urns in such a way that each cell contains at most one ball. Let Mt be the number of urns containing exactly t balls (t = 0, 1, •••, k). In the paper, the distribution of Mt, its moments and moment-generating function are obtained. The derivation of the last two seems to be new.

Keywords

MOMENT GENERATING FUNCTIONDISTRIBUTIONINCLUSION-EXCLUSION PRINCIPLEMOMENTSRESTRICTED OCCUPANCY PROBLEMS
Type
Short Communications
Information
Journal of Applied Probability , Volume 19 , Issue 3 , September 1982 , pp. 707 - 711
Copyright
Copyright © Applied Probability Trust 1982 

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References

Freund, J. E. and Pozner, A. N. (1956) Some results on restricted occupancy theory. Ann. Math. Statist. 27, 537–540.Google Scholar
Johnson, N. L. and Kotz, S. (1977) Urn Models and Their Applications. Wiley, New York.Google Scholar