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

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  • Doerr, Benjamin

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.

Suggested Citation

  • Doerr, Benjamin, 2018. "An elementary analysis of the probability that a binomial random variable exceeds its expectation," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 67-74.
    • Handle: RePEc:eee:stapro:v:139:y:2018:i:c:p:67-74
    DOI: 10.1016/j.spl.2018.03.016
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    References listed on IDEAS

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    1. Pelekis, Christos & Ramon, Jan, 2016. "A lower bound on the probability that a binomial random variable is exceeding its mean," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 305-309.
    2. Greenberg, Spencer & Mohri, Mehryar, 2014. "Tight lower bound on the probability of a binomial exceeding its expectation," Statistics & Probability Letters, Elsevier, vol. 86(C), pages 91-98.
    3. R. Kaas & J.M. Buhrman, 1980. "Mean, Median and Mode in Binomial Distributions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 34(1), pages 13-18, March.
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    Cited by:

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    Keywords

    Lower bounds; Binomial tail;

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