# Probability mass function

Evaluación | Biopsicología | Comparativo | Cognitivo | Del desarrollo | Idioma | Diferencias individuales | Personalidad | Filosofía | Social | Métodos | Estadística | Clínico | Educativo | Industrial | Artículos profesionales | Psicología mundial | Estadística: Método científico · Métodos de búsqueda · Diseño experimental · cursos de pregrado de estadistica · Pruebas estadísticas · Teoría de juego · Decision theory In probability theory, a probability mass function (abbreviated pmf) gives the probability that a discrete random variable is exactly equal to some value. A probability mass function differs from a probability density function in that the values of the latter, defined only for continuous random variables, are not probabilities; bastante, its integral over a set of possible values of the random variable is a probability. Mathematical description Suppose that X is a discrete random variable, taking values on some countable sample space S ⊆ R. Then the probability mass function fX(x)  for X is given by Note that this explicitly defines fX(x)  for all real numbers, including all values in R that X could never take; en efecto, it assigns such values a probability of zero. (Alternativamente, think of Pr(X = x)  como 0 when xRS.) The discontinuity of probability mass functions reflects the fact that the cumulative distribution function of a discrete random variable is also discontinuous. Where it is differentiable (es decir. where xRS) the derivative is zero, just as the probability mass function is zero at all such points. Examples A simple example of a probability mass function is the following. Suppose that X is the outcome of a single coin toss, assigning 0 to tails and 1 to heads. The probability that X = x is just 0.5 on the state space {0, 1} (this is a Bernoulli random variable), and hence the probability mass function is Probability mass functions may also be defined for any discrete random variable, including constant, binomial (including Bernoulli), negative binomial, Poisson, geometric and hypergeometric random variables. nl:kansfunctie This page uses Creative Commons Licensed content from Wikipedia (ver autores).

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