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1 results

  • Probabilities of Competing Binomial Random Variables

  • Part of
  • Wenbo V. Li, Vladislav V. Vysotsky
  • Journal:
    Journal of Applied Probability / Volume 49 / Issue 3 / September 2012
    Published online by Cambridge University Press:
    04 February 2016, pp. 731-744
    Print publication:
    September 2012
    • Article
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  • Suppose that both you and your friend toss an unfair coin n times, for which the probability of heads is equal to α. What is the probability that you obtain at least d more heads than your friend if you make r additional tosses? We obtain asymptotic and monotonicity/convexity properties for this competing probability as a function of n, and demonstrate surprising phase transition phenomenon as the parameters d, r, and α vary. Our main tools are integral representations based on Fourier analysis.