En teoría de la probabilidad y estadística, la distribución de probabilidad de una variable aleatoria es una función que asigna a cada suceso definido sobre la variable aleatoria la probabilidad de que dicho suceso ocurra. La distribución de probabilidad está definida sobre el conjunto de todos los sucesos, cada uno de los sucesos es el rango de valores de la variable aleatoria. La distribución de probabilidad está completamente especificada por la función de distribución, cuyo valor en cada x real es la probabilidad de que la variable aleatoria sea menor o igual que x.

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In probability and statistics, a probability distribution is a mathematical description of a random phenomenon in terms of the probabilities of events. Examples of random phenomena include the results of an experiment or survey. A probability distribution is defined in terms of an underlying sample space, which is the set of all possible outcomes of the random phenomenon being observed. The sample space may be the set of real numbers or a higher-dimensional vector space, or it may be a list of non-numerical values; for example, the sample space of a coin flip would be . Probability distributions are generally divided into two classes. A discrete probability distribution can be encoded by a list of the probabilities of the outcomes, known as a probability mass function. On the other hand, in a continuous probability distribution, the probability of any individual outcome is 0. Continuous probability distributions can often be described by probability density functions; however, more complex experiments, such as those involving stochastic processes defined in continuous time, may demand the use of more general probability measures. In applied probability, a probability distribution can be specified in a number of different ways, often chosen for mathematical convenience: \n* by supplying a valid or \n* by supplying a valid cumulative distribution function or survival function \n* by supplying a valid hazard function \n* by supplying a valid characteristic function \n* by supplying a rule for constructing a new random variable from other random variables whose joint probability distribution is known. A probability distribution whose sample space is the set of real numbers is called univariate, while a distribution whose sample space is a vector space is called 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 vector—a list of two or more random variables—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.

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