probability theoryand 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:
probability mass function"f" of this distribution is
expected valueof a Bernoulli random variable "X" is , and its varianceis
kurtosisgoes to infinity for high and low values of "p", but for the Bernoulli distribution has a lower kurtosis than any other probability distribution, namely -2.
The Bernoulli distribution is a member of the
*If are independent, identically distributed (
i.i.d.) random variables, all Bernoulli distributed with success probability p, then ( binomial distribution).
Categorical distributionis the generalization of the Bernoulli distribution for variables with any constant number of discrete values.
Beta distributionis the conjugate priorof the Bernoulli distribution.
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Bernoulli distribution — noun a theoretical distribution of the number of successes in a finite set of independent trials with a constant probability of success • Syn: ↑binomial distribution • Topics: ↑statistics • Hypernyms: ↑distribution, ↑statistical distribution * *… … Useful english dictionary
Bernoulli distribution — Statistics. See binomial distribution. [named after Jakob BERNOULLI] * * * … Universalium
Bernoulli distribution — noun A discrete probability distribution, which takes value 1 with success probability and value 0 with failure probability … Wiktionary
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Bernoulli — can refer to: *any one or more of the Bernoulli family of Swiss mathematicians in the eighteenth century, including: ** Daniel Bernoulli (1700–1782), developer of Bernoulli s principle ** Jakob Bernoulli (1654–1705), also known as Jean or Jacques … Wikipedia
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