A lower bound on the probability that a binomial random variable is exceeding its mean

TL;DR

This paper establishes a lower bound on the probability that a binomial random variable exceeds its mean, using estimates on mean absolute deviation and tail conditional expectation.

Contribution

It introduces a novel lower bound for binomial tail probabilities based on new analytical estimates.

Findings

Derived a lower bound for binomial tail probability

Utilized mean absolute deviation and tail conditional expectation in proofs

Provides insights into binomial distribution behavior

Abstract

We provide a lower bound on the probability that a binomial random variable is exceeding its mean. Our proof employs estimates on the mean absolute deviation and the tail conditional expectation of binomial random variables.