An elementary analysis of the probability that a binomial random variable exceeds its expectation

作者：Doerr Benjamin^*

来源：Statistics & Probability Letters, 2018, 139: 67-74.

DOI：10.1016/j.spl.2018.03.016

• Lower bounds
• Binomial tail

We give an elementary proof of the fact that a binomial random variable X with parameters n and 0.29/n <= p < 1 with probability at least 1/4 strictly exceeds its expectation. We also show that for 1/n <= p < 1 - 1/n, X exceeds its expectation by more than one with probability at least 0.0370. Both probabilities approach 1/2 when np and n(1 - p) tend to infinity.

• 出版日期2018-8