probability of success
The Bernoulli distribution is a discrete probability distribution with probability function given by:
subject to the following conditions:
The Bernoulli distribution comes about as a consequence of a single Bernoulli trial. Success of the Bernoulli trial is indicated with x=1 and failure is indicated with x=0, where a success occurs with probability p. The parameter p is also referred to as the Bernoulli probability parameter.
Note that the Bernoulli command is inert and should be used in combination with the RandomVariable command.
X ≔ RandomVariable⁡Bernoulli⁡p:
Evans, Merran; Hastings, Nicholas; and Peacock, Brian. Statistical Distributions. 3rd ed. Hoboken: Wiley, 2000.
Johnson, Norman L.; and Kotz, Samuel; and Balakrishnan, N. Continuous Univariate Distributions. 2nd ed. 2 vols. Hoboken: Wiley, 1995.
Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.
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