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

Iosif Pinelis

Statistics & Probability Letters, 2021, vol. 179, issue C

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.

Keywords: Binomial distribution; Probability inequalities; Exact bounds (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.spl.2021.109224

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