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

Svante Janson

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arXiv · 2009.13781

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

Svante Janson

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Abstract

Consider the probability that a binomial random variable Bi$(n,m/n)$ with integer expectation $m$ is at most its expectation. Chv\'atal 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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Svante Janson. 2020-09-29. On the probability that a binomial variable is at most its expectation. https://arxiv.org/abs/2009.13781

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