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Bernoulli distribution

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

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 math and value 0 with failure probability math. So if X is a random variable with this distribution, we have:

math

The probability mass function f of this distribution is

math

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

math

The Bernoulli distribution is a member of the exponential family.

[edit] Related distributions

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

[edit] See also

fr:Distribution de Bernoullihe:התפלגות ברנולי nl:Bernoulli-verdelingfi:Bernoullin jakauma zh:伯努利分布

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