Bernoullifordeling

The Bernoulli distribution is a discrete probability distribution that models a single trial of a random experiment with exactly two possible outcomes, typically labeled as "success" and "failure". It is named after the Swiss mathematician Jacob Bernoulli. The distribution is characterized by a single parameter, p, which represents the probability of success in a single trial. The probability mass function (PMF) of the Bernoulli distribution is given by:

P(X = x) = p^x * (1 - p)^(1 - x)

for x in {0, 1}, where X is a random variable that follows the Bernoulli distribution.

The Bernoulli distribution is a special case of the binomial distribution, which models the number of successes in a fixed number of independent Bernoulli trials. The mean (expected value) of a Bernoulli random variable is p, and the variance is p(1 - p). The distribution is widely used in statistics, probability theory, and various fields of science and engineering to model binary outcomes and make inferences about population parameters.