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On the distribution of the time required to remove white balls from an URN

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Abstract

Balls are removed one-at-a-time at equal time intervals from an urn initially containingw 0 white balls and a large number b of black balls and each black or white ball is immediately replaced by a black ball. The distribution of the number of white balls remaining aftert iterations (under certain limiting operations) is taken from the literature. The problem is to use this result to find the time required to remove a fixed number of white ballsw 1 from the urn. We then find the mean and variance of this distribution and also look at the special case whenw 1 =w 0.

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Authors and Affiliations

  1. Mathematics Department, University of California at Santa Barbara, 93106, Santa Barbara, CA, USA

    Milton Sobel

  2. Health and Safety Research Division, Oak Ridge National Laboratory, 37831, Oak Ridge, TN, USA

    S. R. Bernard

  3. Mathematical Sciences Section, Engineering Physics and Mathematica Division, Oak Ridge National Laboratory, 37831, Oak Ridge, TN, USA

    V. R. R. Uppuluri

Authors
  1. Milton Sobel
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  2. S. R. Bernard
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  3. V. R. R. Uppuluri
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Sobel, M., Bernard, S.R. & Uppuluri, V.R.R. On the distribution of the time required to remove white balls from an URN. Bltn Mathcal Biology 47, 791–797 (1985). https://doi.org/10.1007/BF02469306

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  • DOI: https://doi.org/10.1007/BF02469306

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