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A generalization of a waiting time problem

Published online by Cambridge University Press:  01 July 2016

B. S. El-Desouky  and
S. A. Hussen
B. S. El-Desouky*
Affiliation:
Faculty of Science, Aswan
S. A. Hussen*
Affiliation:
Faculty of Science, Aswan
*
∗Postal address for both authors: Department of Mathematics, Faculty of Science, Aswan, Egypt.
∗Postal address for both authors: Department of Mathematics, Faculty of Science, Aswan, Egypt.
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Abstract

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An urn contains m types of balls of unequal numbers. Let ni be the number of balls of type i, i = 1, 2, …, m. Balls are drawn with replacement until first duplication. In the case of finite memory of order k, the distribution of Ym,k, the number of drawings required, is discussed. Special cases are obtained.

Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 22 , Issue 3 , September 1990 , pp. 758 - 760
Copyright
Copyright © Applied Probability Trust 1990 

References

[1] Arnold, B. C. (1972) The waiting time until first duplication. J. Appl. Prob. 9, 841–846.Google Scholar
[2] Comtet, L. (1972) Nombres de Stirling généraux et fonctions symetriques. C. R. Acad. Sci. Paris A 275, 747–750.Google Scholar
[3] Comtet, L. (1974) Advanced Combinatorics. D. Reidel, Dordrecht.Google Scholar
[4] Mccabe, B. (1979) Problem E. 2263. Amer. Math. Monthly 77, 1008.Google Scholar