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arXiv · 1010.4063

Probabilities of competing binomial random variables

Wenbo V. Li·Vladislav V. Vysotsky
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Abstract

Suppose you and your friend both do $n$ tosses of an unfair coin with probability of heads equal to $\alpha$. What is the behavior of 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 phenomenons as parameters $ d, r$ and $\alpha$ vary. Our main tools are integral representations based on Fourier analysis.

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Wenbo V. Li, Vladislav V. Vysotsky. 2010-10-19. Probabilities of competing binomial random variables. https://arxiv.org/abs/1010.4063

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