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[[Image:Discrete probability distrib.png|right|thumb|The graph of a probability mass function. All the values of this function must be non-negative and sum up to 1.]]
In [[probability theory]], a '''probability mass function''' (abbreviated '''pmf''') is a function that 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]] (abbreviated '''pdf''') in that the values of a pdf, defined only for [[continuous random variable]]s, are not probabilities as such. Instead, the integral of a pdf over a range of possible values <nowiki>[</nowiki>''a'', ''b'') gives the probability of the random variable falling within that range.
==Mathematical description==
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