Bernoulli distribution

A discrete probability distribution for a binary outcome, assigning probability p to success and 1−p to failure. Its single parameter p determines the probabilities of both outcomes.

Probability mass function: A function that assigns probabilities to the possible values of a discrete random variable. The Bernoulli distribution is specified by assigning mass p to 1 and 1−p to 0.
Random variable: A function that assigns a numerical value to each outcome of a random experiment. The Bernoulli distribution describes the values of a random variable with two possible outcomes.
Bernoulli trial: A random experiment with two outcomes and a fixed probability of success. A Bernoulli trial produces one observation governed by the distribution.
Categorical distribution: A discrete distribution over a finite set of categories, each assigned a probability. It generalizes Bernoulli outcomes from two categories to any finite number.
Maximum likelihood estimation: A method that estimates model parameters by maximizing the likelihood of observed data. For independent Bernoulli observations, the maximum-likelihood estimate of p is the observed success fraction.
Indicator random variable: A random variable equal to 1 when a specified event occurs and 0 otherwise. Coding success as 1 and failure as 0 gives the standard Bernoulli variable.
Discrete probability distribution: A probability distribution over a finite or countably infinite set of values. Bernoulli is the simplest nondegenerate distribution on a finite outcome set.
Binomial distribution: The distribution of the number of successes in a fixed number of independent trials with equal success probability. It sums independent Bernoulli outcomes when counting successes across repeated trials.
Discrete uniform distribution: A distribution assigning equal probability to every value in a finite set. It matches Bernoulli only when both outcomes have probability one-half.
Fisher information: A measure of how much data from a statistical model reveals about an unknown parameter. A Bernoulli observation carries information about p that increases near balanced probabilities.

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