In [[probability theory]] and [[statistics]], a '''probability distribution''', also known as a probability measure, 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.
