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Bernoulli
Probability mass function
Cumulative distribution function
Parameters (real)
Support
Template:Probability distribution/link mass
cdf
Mean
Median N/A
Mode
Variance
Skewness
Kurtosis
Entropy
mgf
Char. func.

In probability theory and statistics, the Bernoulli distribution, named after Swiss scientist Jakob Bernoulli, is a discrete probability distribution, which takes value 1 with success probability and value 0 with failure probability . So if X is a random variable with this distribution, we have:

The probability mass function f of this distribution is

The expected value of a Bernoulli random variable X is , and its variance is

The Bernoulli distribution is a member of the exponential family.

Related distributions[edit | edit source]

  • If are independent, identically distributed random variables, all Bernoulli distributed with success probability p, then (binomial distribution).

See also[edit | edit source]

es:Distribución de Bernoulli fr:Distribution de Bernoulli he:התפלגות ברנולי nl:Bernoulli-verdeling fi:Bernoullin jakauma zh:伯努利分布

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