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arXiv · 2108.04916

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

Iosif Pinelis
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Abstract

Let $X$ be a random variable distributed according to the binomial distribution with parameters $n$ and $p$. It is shown that $P(X>EX)\ge1/4$ if $1>p\ge c/n$, where $c:=\ln(4/3)$, the best possible constant factor.

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Iosif Pinelis. 2021-08-10. Best lower bound on the probability of a binomial exceeding its expectation. https://arxiv.org/abs/2108.04916

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