Bernoulli distribution

7.5

A model for one yes-or-no event with a fixed chance of success

noun
/bərˈnuːli dɪsˈtrɪbjuːʃən/

Specialized

: distribución de Bernoulli

The Bernoulli distribution models a coin flip, where there are only two outcomes: heads or tails.

Examples

Or, to think about it differently, we start with the Bernoulli distribution that's very skewed.
So remember, the Bernoulli distribution has a PMF which is part of the canonical exponential family.
In a Bernoulli distribution, the probability of success remains constant for each trial.
Researchers often use the Bernoulli distribution to analyze yes/no survey responses.

Surface Forms

Bernoulli distribution singular

Bernoulli distributions plural

Morphology

Bernoulli + distribution

This is an eponymous technical term: 'Bernoulli' is a proper name with no independent lexical meaning that signals 'two outcomes' or 'fixed success probability', while 'distribution' only indicates a general probabilistic concept. A B1 learner who knows both words would not be able to derive the specific two-outcome/fixed-probability meaning from the constituents, so the expression is not compositionally transparent.

Etymology

The noun Bernoulli distribution comes from the Bernoulli family, especially Jacob Bernoulli, who studied simple 'yes-or-no' experiments like a 'coin flip'. Think of one coin flip: it can be success or failure, and Jacob used math to give a fixed chance for success, so the term now means the probability of just two outcomes.