On the waiting time till some patterns occur in i.i.d. sequences

2013/02/20 by Urszula Ostaszewska, Ostaszewska, Urszula, Krzysztof Zajkowski +1
Mathematics · #60E05 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60E05

paper · pdf · doi:10.48550/arxiv.1302.4859

9 pages

arxiv created 2013/02/20 · arxiv updated 2013/02/21

Abstract

In this paper we present some general solution of the system of linear equations formed by Guibas and Odlyzko in Th.3.3 \citeGui. We derive probabilities for given patterns to be first to appear in random text and the expected waiting time till one of them is observed and also till one of them occurs given it is known which pattern appears first.

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