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

Benjamin Doerr

doi:10.1016/j.spl.2018.03.016

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

Benjamin Doerr

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	67-74
Number of pages	8
Journal	Statistics and Probability Letters
Volume	139
DOIs	https://doi.org/10.1016/j.spl.2018.03.016
Publication status	Published - 1 Aug 2018

Keywords

Binomial tail
Lower bounds

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10.1016/j.spl.2018.03.016

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title = "An elementary analysis of the probability that a binomial random variable exceeds its expectation",

abstract = "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.",

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AB - 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.

KW - Binomial tail

KW - Lower bounds

UR - https://www.scopus.com/pages/publications/85045265863

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DO - 10.1016/j.spl.2018.03.016

M3 - Article

AN - SCOPUS:85045265863

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VL - 139

SP - 67

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JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

ER -

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

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Keywords

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