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

08/10/2021

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by   Iosif Pinelis, et al.

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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.