On the probability that a binomial variable is at most its expectation

2020/09/29 by Janson, Svante
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2009.13781

Abstract

Consider the probability that a binomial random variable Bi(n,m/n) with integer expectation m is at most its expectation. Chvátal conjectured that for any given n, this probability is smallest when m is the integer closest to 2n/3. We show that this holds when n is large.

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