Bernoulli distribution
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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 distributionsEdit
- If are independent, identically distributed random variables, all Bernoulli distributed with success probability p, then (binomial distribution).
See alsoEdit
fr:Distribution de Bernoullihe:התפלגות ברנולי nl:Bernoulli-verdelingfi:Bernoullin jakauma zh:伯努利分布
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