Best lower bound on the probability of a binomial exceeding its expectation

2021/08/10 by Pinelis, Iosif
#60E15 #62E15 #FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2108.04916

Abstract

Let X be a random variable distributed according to the binomial distribution with parameters n and p. It is shown that P(X>EX)≥1/4 if 1>p≥ c/n, where c:=ln(4/3), the best possible constant factor.

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