# Bernoulli distribution

## Probability distribution modeling a coin toss which need not be fair / From Wikipedia, the free encyclopedia

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In probability theory and statistics, the **Bernoulli distribution**, named after Swiss mathematician Jacob Bernoulli,[1] is the discrete probability distribution of a random variable which takes the value 1 with probability and the value 0 with probability . Less formally, it can be thought of as a model for the set of possible outcomes of any single experiment that asks a yes–no question. Such questions lead to outcomes that are boolean-valued: a single bit whose value is success/yes/true/one with probability *p* and failure/no/false/zero with probability *q*. It can be used to represent a (possibly biased) coin toss where 1 and 0 would represent "heads" and "tails", respectively, and *p* would be the probability of the coin landing on heads (or vice versa where 1 would represent tails and *p* would be the probability of tails). In particular, unfair coins would have

**Quick facts: Parameters, Support, PMF, CDF, Mean...**▼

Probability mass function
Three examples of Bernoulli distribution: and
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Part of a series on statistics |

Probability theory |
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The Bernoulli distribution is a special case of the binomial distribution where a single trial is conducted (so *n* would be 1 for such a binomial distribution). It is also a special case of the **two-point distribution**, for which the possible outcomes need not be 0 and 1.