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The use of random variables is most common in probability and statistics, where they are used to quantify outcomes of random occurrences. Tag: Reverted |
Gmarmstrong (talk | contribs) Reverted good faith edits by 74.13.240.170 (talk): Doesn't make sense in context; also appears to be ripped from Quizlet flashcards |
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===Extensions===
The term "random variable" in statistics is traditionally limited to the [[real number|real-valued]] case (<math>E=\mathbb{R}</math>). In this case, the structure of the real numbers makes it possible to define quantities such as the [[expected value]] and [[variance]] of a random variable, its [[cumulative distribution function]], and the [[moment (mathematics)|moment]]s of its distribution
However, the definition above is valid for any [[measurable space]] <math>E</math> of values. Thus one can consider random elements of other sets <math>E</math>, such as random [[Boolean-valued function|Boolean value]]s, [[categorical variable|categorical value]]s, [[Covariance matrix#Complex random vectors|complex numbers]], [[random vector|vector]]s, [[random matrix|matrices]], [[random sequence|sequence]]s, [[Tree (graph theory)|tree]]s, [[random compact set|set]]s, [[shape]]s, [[manifold]]s, and [[random function|function]]s. One may then specifically refer to a ''random variable of [[data type|type]] <math>E</math>'', or an ''<math>E</math>-valued random variable''.
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