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2 results

  • Maximal Percentages in Pólya's Urn

  • Part of
  • Ernst Schulte-Geers, Wolfgang Stadje
  • Journal:
    Journal of Applied Probability / Volume 52 / Issue 1 / March 2015
    Published online by Cambridge University Press:
    30 January 2018, pp. 180-190
    Print publication:
    March 2015
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  • We show that the supremum of the successive percentages of red balls in Pólya's urn model is almost surely rational, give the set of values that are taken with positive probability, and derive several exact distributional results for the all-time maximal percentage.

  • Counts of Failure Strings in Certain Bernoulli Sequences

  • Part of
  • Lars Holst
  • Journal:
    Journal of Applied Probability / Volume 44 / Issue 3 / September 2007
    Published online by Cambridge University Press:
    14 July 2016, pp. 824-830
    Print publication:
    September 2007
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  • In a sequence of independent Bernoulli trials the probability for success in the kth trial is pk, 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 pk = 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.