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Bernoulli Distribution (Bernoulli₍p₎) ○◂｜Definition｜1st｜20260604231540-00-⌔
Bernoulli distribution - Wikipedia
Bernoulli distribution
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
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 1.2
Printed 2026-06-28.
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Link to original Footnotes
Uspensky, James Victor (1937). Introduction to Mathematical Probability. New York: McGraw-Hill. p. 45. OCLC 996937. ↩
Dekking, Frederik; Kraaikamp, Cornelis; Lopuhaä, Hendrik; Meester, Ludolf (9 October 2010). A Modern Introduction to Probability and Statistics (1 ed.). Springer London. pp. 43–48. ISBN 9781849969529. ↩
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