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Counts of Failure Strings in Certain Bernoulli Sequences

  • Lars Holst (a1)

Abstract

In a sequence of independent Bernoulli trials the probability for success in the kth trial is p k , k = 1, 2, …. The number of strings with a given number of failures between two subsequent successes is studied. Explicit expressions for distributions and moments are obtained for the case in which p k = a/(a + b + k − 1), a > 0, b ≥ 0. Also, the limit behaviour of the longest failure string in the first n trials is considered. For b = 0, the strings correspond to cycles in random permutations.

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Copyright

Corresponding author

Postal address: Department of Mathematics, Royal Institute of Technology, SE-10044 Stockholm, Sweden. Email address: lholst@math.kth.se

References

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Holst, L. (2006). On the number of consecutive successes in Bernoulli trials. Preprint.
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