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The waiting time until first duplication

Published online by Cambridge University Press:  14 July 2016

Barry C. Arnold
Barry C. Arnold*
Affiliation:
Iowa State University, Arnes, Iowa
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Abstract

Balls are drawn with replacement from an urn containing m distinguishable balls until a match is noted. The distribution of the number of drawings required is considered in the case where only the last k balls drawn are remembered. The asymptotic behavior of this distribution, as m and k become large, is investigated. Two further variants of the problem are suggested.

Keywords

BIRTHDAY PROBLEMDISCRETE WAITING TIMEFINITE MEMORYFIRST MATCHLIMITING DENSITIES

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 9 , Issue 4 , December 1972 , pp. 841 - 846
Copyright
Copyright © Applied Probability Trust 1972 

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References

[1] Feller, W. (1968) An Introduction to Probability Theory and its Appliciations. Vol. I, 3rd ed. John Wiley, New York.Google Scholar
[2] Mccabe, B. (1970) Problem E. 2263. Amer. Math. Monthly 77, 1008.Google Scholar