Editing Probability mass function (section)

{{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]] and [[statistics]], a '''probability mass function''' (sometimes called ''probability function'' or ''frequency function''<ref>[https://online.stat.psu.edu/stat414/lesson/7/7.2 7.2 - Probability Mass Functions | STAT 414 - PennState - Eberly College of Science]</ref>) 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 probability 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|continuous probability density function]] (PDF) in that the latter is associated with continuous rather than discrete random variables. A continuous 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>

The value of the random variable having the largest probability mass is called the [[mode (statistics)|mode]].