In probability and statistics, a probability distribution assigns a probability to each measurable subset of the possible outcomes of a random experiment, survey, or procedure of statistical inference.

In applied probability, a probability distribution can be specified in a number of different ways, often chosen for mathematical convenience:

by supplying a valid probability mass function or probability density function

by supplying a valid cumulative distribution function or survival function

by supplying a valid hazard function

by supplying a valid characteristic function by supplying a rule for constructing a new random variable from other random variables whose joint probability distribution is known.

A probability distribution can either be univariate or multivariate. A univariate distribution gives the probabilities of a single random variable taking on various alternative values; a multivariate distribution (a joint probability distribution) gives the probabilities of a random vectorâ€”a set of two or more random variablesâ€”taking on various combinations of values. Important and commonly encountered univariate probability distributions include the binomial distribution, the hypergeometric distribution, and the normal distribution. The multivariate normal distribution is a commonly encountered multivariate distribution.