Title

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

Document Type

Article

Publication Date

12-2021

Department

Department of Mathematical Sciences

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.

Publication Title

Statistics & Probability Letters

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