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Bernoulli random variable (Definition)

$ X$ is a Bernoulli random variable with parameter $ p$ if

$ f_X(x) = p^x (1-p)^{1-x}$, $ x=\{0,1\}$

Parameters:

$ \star$
$ p \in [0,1]$

Syntax:

$ X\sim Bernoulli(p)$

Notes:

  1. $ X$ represents the number of successful results in a Bernoulli trial. A Bernoulli trial is an experiment in which only two outcomes are possible: success, with probability $ p$, and failure, with probability $ 1-p$.
  2. $ E[X] = p$
  3. $ Var[X] = p(1-p)$
  4. $ M_X(t) = p e^t + (1-p)$



"Bernoulli random variable" is owned by Riemann.
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See Also: binomial distribution, geometric distribution

Other names:  Bernoulli distribution
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Cross-references: outcomes, number, represents, syntax, parameter
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This is version 2 of Bernoulli random variable, born on 2001-10-26, modified 2001-10-26.
Object id is 517, canonical name is BernoulliRandomVariable.
Accessed 13005 times total.

Classification:
AMS MSC: 60-00 (Probability theory and stochastic processes :: General reference works )
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