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

Svante Janson

Statistics & Probability Letters, 2021, vol. 171, issue C

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.

Keywords: Binomial probabilities; Edgeworth expansions; Median (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spl.2020.109020

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