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Binomial

In: Statistical Distributions

Author

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  • Nick T. Thomopoulos

    (Illinois Institute of Technology, Stuart School of Business)

Abstract

Some historians give the first use of the binomial distribution to Jakob Bernoulli who was a prominent Swiss mathematician in the 1600s. The binomial distribution applies when a number of trials of an experiment is run and only two outcomes are noted on each trial, success and failure, and the probability of the outcomes remain the same over all of the trials. This happens, for example, when a roll of two dice is run five times and the success per run is when the number of dots is two, say. The probability of a success per run remains constant, the number of trials in five, and the probability of a success per trial is p = 1/36. The random variable, denoted as x, for this scenario is the number of successes in the five trials, and this could be: x = 0, 1, 2, 3, 4, 5. The chapter lists the probability distribution of the random variable x. The mean, variance, standard deviation and mode of x is also given. When p is not known, it can be estimated using sample data, and even when no sample data is provided, an estimate of p can be obtained.

Suggested Citation

  • Nick T. Thomopoulos, 2017. "Binomial," Springer Books, in: Statistical Distributions, chapter 0, pages 119-126, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-65112-5_14
    DOI: 10.1007/978-3-319-65112-5_14
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