Editing Probability distribution (section)

{{short description|Mathematical function for the probability a given outcome occurs in an experiment}}
{{other uses|Distribution (disambiguation){{!}}Distribution}}

{{Probability fundamentals}}

In [[probability theory]] and [[statistics]], a '''probability distribution''' is a [[Function (mathematics)|function]] that gives the probabilities of occurrence of possible '''events''' for an [[Experiment (probability theory)|experiment]].<ref name=":02">{{Cite book|title=The Cambridge dictionary of statistics|last=Everitt | first = Brian |date=2006|publisher=Cambridge University Press|isbn=978-0-511-24688-3 |edition=3rd|location=Cambridge, UK|oclc=161828328}}</ref><ref>{{Cite book|title=Basic probability theory|last=Ash, Robert B.|date=2008|publisher=Dover Publications |isbn=978-0-486-46628-6 |edition=Dover |location=Mineola, N.Y. |pages=66–69|oclc=190785258}}</ref> It is a mathematical description of a [[Randomness|random]] phenomenon in terms of its [[sample space]] and the [[Probability|probabilities]] of [[Event (probability theory)|events]] ([[subset]]s of the sample space).<ref name=":1">{{cite book|title=Probability and statistics: the science of uncertainty|last1=Evans |first1=Michael |date=2010|publisher=W.H. Freeman and Co|last2=Rosenthal |first2=Jeffrey S. |isbn=978-1-4292-2462-8 |edition=2nd|location=New York|pages=38|oclc=473463742}}</ref>

For instance, if {{mvar|X}} is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of {{mvar|X}} would take the value 0.5 (1 in 2 or 1/2) for {{math|1=''X'' = heads}}, and 0.5 for {{math|1=''X'' = tails}} (assuming that [[fair coin|the coin is fair]]). More commonly, probability distributions are used to compare the relative occurrence of many different random values.

Probability distributions can be defined in different ways and for discrete or for continuous variables. Distributions with special properties or for especially important applications are given specific names.