Random variable: Difference between revisions

Revision as of 03:38, 16 October 2023

Revision as of 09:31, 18 October 2023

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{{Probability fundamentals}}

A '''random variable''' (also called '''random quantity''', '''aleatory variable''', or '''stochastic variable''') is a mathematical formalization of a quantity or object which depends on [[randomness|random]] events.<ref name=":2">{{cite book|last1=Blitzstein|first1=Joe|title=Introduction to Probability|last2=Hwang|first2=Jessica|date=2014|publisher=CRC Press|isbn=9781466575592}}</ref> The term 'random variable' can be misleading as itits mathematical definition is not actually random nor a variable,<ref>{{Cite book |last=Deisenroth |first=Marc Peter |url=https://www.worldcat.org/oclc/1104219401 |title=Mathematics for machine learning |date=2020 |others=A. Aldo Faisal, Cheng Soon Ong |isbn=978-1-108-47004-9 |___location=Cambridge, United Kingdom |oclc=1104219401 |publisher=Cambridge University Press}}</ref> but rather it is a [[function (mathematics)|function]] from possible [[Outcome (probability)|outcomes]] (e.g., the possible upper sides of a flipped coin such as heads <math>H</math> and tails <math>T</math>) in a [[sample space]] (e.g., the set <math>\{H,T\}</math>) to a [[measurable space]] (e.g., <math>\{-1,1\}</math> in which 1 is corresponding to <math>H</math> and −1 is corresponding to <math>T</math>, respectively), often to the real numbers.

[[File:Random Variable as a Function-en.svg|thumb|This graph shows how random variable is a function from all possible outcomes to real values. It also shows how random variable is used for defining probability mass functions.]]