Probability mass function: Difference between revisions

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{{Short description|Discrete-variable probability distribution}}

[[Image:Discrete probability distrib.svg|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|probability theory]] and [[statistics]], a '''probability mass function''' ('''PMF''') is a function that gives the probability that a [[discrete random variable]] is exactly equal to some value.<ref>{{cite book|author=Stewart, William J.|title=Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling|publisher=Princeton University Press|year=2011|isbn=978-1-4008-3281-1|page=105|url=https://books.google.com/books?id=ZfRyBS1WbAQC&pg=PT105}}</ref> Sometimes it is also known as the discrete density function. The probability mass function is often the primary means of defining a [[discrete probability distribution]], and such functions exist for either [[Scalar variable|scalar]] or [[multivariate random variable]]s whose [[Domain of a function|___domain]] is discrete.

A probability mass function differs from a [[probability density function]] (PDF) in that the latter is associated with continuous rather than discrete random variables. A PDF must be [[integration (mathematics)|integrated]] over an interval to yield a probability.<ref name=":0">{{Cite book|title=A modern introduction to probability and statistics : understanding why and how|date=2005|publisher=Springer|others=Dekking, Michel, 1946-|isbn=978-1-85233-896-1|___location=London|oclc=262680588}}</ref>