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The Number of Two Consecutive Successes in a Hoppe-Pólya Urn

Part of: Special processes Combinatorial probability

Published online by Cambridge University Press:  14 July 2016

Lars Holst
Lars Holst*
Affiliation:
Royal Institute of Technology
*
∗Postal address: Department of Mathematics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden. Email address: [email protected]
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Abstract

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In a sequence of independent Bernoulli trials the probability of success in the kth trial is pk = a / (a + b + k − 1). An explicit formula for the binomial moments of the number of two consecutive successes in the first n trials is obtained and some consequences of it are derived.

Keywords

Bernoulli trialbinomial momentHoppe urnoverlapping indicatorsPólya urnrecordsrandom permutation

MSC classification

Secondary: 60C05: Combinatorial probability 60K99: None of the above, but in this section
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 3 , September 2008 , pp. 901 - 906
Copyright
Copyright © Applied Probability Trust 2008 

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