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How Many Random Digits Are Required until Given Sequences Are Obtained?

Gunnar Blom and Daniel Thorburn
Journal of Applied Probability
Vol. 19, No. 3 (Sep., 1982), pp. 518-531
DOI: 10.2307/3213511
Stable URL: http://www.jstor.org/stable/3213511
Page Count: 14
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How Many Random Digits Are Required until Given Sequences Are Obtained?
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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.

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