Probabilities of competing binomial random variables

Wenbo V. Li, Vladislav V. Vysotsky

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)731-744
Number of pages14
JournalJournal of Applied Probability
Volume49
Issue number3
DOIs
StatePublished - Sep 2012

Fingerprint

Random variable
Unfair
Fourier Analysis
Integral Representation
Monotonicity
Convexity
Phase Transition
Vary
Demonstrate
Random variables
Integral
Phase transition

Keywords

  • Binomial random variable
  • Coin tossing
  • Competing random variables
  • Number of successes
  • Phase transition
  • Probability of winning

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Probabilities of competing binomial random variables. / Li, Wenbo V.; Vysotsky, Vladislav V.

In: Journal of Applied Probability, Vol. 49, No. 3, 09.2012, p. 731-744.

Research output: Contribution to journalArticle

Li, Wenbo V. ; Vysotsky, Vladislav V. / Probabilities of competing binomial random variables. In: Journal of Applied Probability. 2012 ; Vol. 49, No. 3. pp. 731-744.
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