Probability mass function: Difference between revisions

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In [[probability theory]], a '''probability mass function''' (abbreviated '''pmf''') gives the probability that a [[discrete random variable|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 variable]]s, are not probabilities; rather, its integral over a set of possible values of the random variable is a probability.

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==Mathematical description==

Suppose that ''X'' is a discrete random variable, taking values on some [[countable]] [[sample space]]  ''S'' ⊆ '''R'''. Then the probability mass function  ''f''_''X''(''x'')  for ''X'' is given by