Combinatorics of geometrically distributed random variables: run statistics

Authors:
Peter J. Grabner;Arnold Knopfmacher;Helmut Prodinger
Affiliations:
Institut für Mathematik A, Technische Universität Graz, Steyrergasse 30, 8010 Graz, Austria;Department of Computational and Applied Mathematics, The John Knopfmacher Centre for Applicable Analysis and Number Theory, University of the Witwatersrand, P.O. Wits, 2050 Johannesburg, South Afr ...;Department of Mathematics, The John Knopfmacher Centre for Applicable Analysis and Number Theory, University of the Witwatersrand, P.O. Wits, 2050 Johannesburg, South Africa
Venue:
Theoretical Computer Science - Latin American theoretical informatics
Year:
2003

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Abstract

For words of length n, generated by independent geometric random variables, we consider the mean and variance, and thereafter the distribution of the number of runs of equal letters in the words. In addition, we consider the mean length of a run as well as the length of the longest run over all words of length n.