Bernoulli distribution

The Bernoulli distribution is a probability distribution. It takes a value of 1 with probability p and a value of 0 with probability 1-p. It is sometimes written as $\operatorname {Ber} (p)$ .^[1] It is used in probability theory and statistics. It is named after a Swiss scientist Jacob Bernoulli.

Overview[change | change source]

A Bernoulli distribution is useful because it can be used to approximate the outcomes of an experiment (such as tossing a coin) as a range of percentages. It represents a "yes or no" type experiment. If the experiment succeeds, then it is given the value 1. If the experiment does not succeed, it is given value 0.^[2] This can be used, for example, in tossing a coin, where "1" means it lands on "heads", and "0" means it lands on "tails" (or the other way around).^[3]

This distribution has only one parameter, the probability of a success (p). In fact, Bernoulli distribution is the binomial distribution with n=1, and n independent and identically distributed Bernoulli distributions also give rise to binomial distribution.