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How many random digits are required until given sequences are obtained?

Published online by Cambridge University Press:  14 July 2016

Gunnar Blom  and
Daniel Thorburn
Gunnar Blom*
Affiliation:
University of Lund
Daniel Thorburn*
Affiliation:
University of Lund
*
∗Postal address: Department of Mathematical Statistics, University of Lund, Box 725, S-220 07 Lund, Sweden.
∗∗Present address: Department of Mathematical Statistics, University of Stockholm, Box 6701, S-113 85 Stockholm, Sweden.
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Abstract

Random digits are collected one at a time until a given k -digit sequence is obtained, or, more generally, until one of several k -digit sequences is obtained. In the former case, a recursive formula is given, which determines the distribution of the waiting time until the sequence is obtained and leads to an expression for the probability generating function. In the latter case, the mean waiting time is given until one of the given sequences is obtained, or, more generally, until a fixed number of sequences have been obtained, either different sequences or not necessarily different ones. Several results are known before, but the methods of proof seem to be new.

Keywords

LEADING NUMBERSOVERLAPRENEWAL PROCESSSTOPPING SEQUENCE
Type
Research Papers
Information
Journal of Applied Probability , Volume 19 , Issue 3 , September 1982 , pp. 518 - 531
Copyright
Copyright © Applied Probability Trust 1982 

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