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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

Smallwikipedialogo.png This page uses content from the English-language version of Wikipedia. The original article was at Bernoulli distribution. The list of authors can be seen in the page history. As with Psychology Wiki, the text of Wikipedia is available under the GNU Free Documentation License.

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