Bernoulli distribution
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| Probability mass function | |
| Cumulative distribution function | |
| Parameters | (real)
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| Template:Probability distribution/link mass |
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| cdf | WikiTeX: latex reported a failure, namely:This is pdfeTeX, Version 3.141592-1.21a-2.2 (Web2C 7.5.4) entering extended mode (./4b49478485a5630999bc736c422cb LaTeX2e <2003/12/01> Babel |
| Mean |
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| Median | N/A |
| Mode |
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| Variance |
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| Skewness |
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| Kurtosis |
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| Entropy |
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| mgf |
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| Char. func. |
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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.
[edit] Related distributions
- If
are independent, identically distributed random variables, all Bernoulli distributed with success probability p, then
(binomial distribution).
[edit] See also
fr:Distribution de Bernoullihe:התפלגות ברנולי nl:Bernoulli-verdelingfi:Bernoullin jakauma zh:伯努利分布
| 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. |















