# Bernoulli distribution

## English

### Etymology

After Swiss mathematician Jacob Bernoulli (1654—1705), one of many noted mathematicians of the Bernoulli family, who made important contributions to the field of probability.

### Noun

1. (statistics) A discrete probability distribution that represents the result of a single trial, taking value 1 with "success" probability ${\displaystyle p}$ and value 0 with "failure" probability ${\displaystyle q=1-p}$.
• 1977 [Wiley], Jean Dickinson Gibbons, Ingram Olkin, Milton Sobel, Selecting and Ordering Populations, 1999, Society for Industrial and Applied Mathematics, Unabridged corrected republication, page 103,
Since both of these distributions involve the same parameter p, the problem under consideration here may be called either selection of the best Bernoulli distribution or selection of the best binomial distribution.
• 1985, R. R. Kinnison, Applied Extreme Value Statistics, Battelle Press, page 26,
A critical factor in the use of Bernoulli distributions is that the parameters of the distribution are known constants.
• 2000, A. Berny, Selection and Reinforcement Learning for Combinatorial Optimization, Marc Schoenauer, Kalyanmoy Deb, Günther Rudolph, Xin Yao, Evelynne Lutton, Juan Julian Merelo, Hans-Paul Schwefel (editors), Parallel Problem Solving from Nature-PPSN VI, 6th International Conference Proceedings, Springer, page 601,
In this paper however, we will only consider the family of Bernoulli distributions.

#### Usage notes

The Bernoulli distribution is a special case of the binomial distribution, which treats an arbitrary number of trials.