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| Probability mass function|
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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 Bernoulli distribution is a member of the exponential family.
- If are independent, identically distributed random variables, all Bernoulli distributed with success probability p, then (binomial distribution).
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