Characteristic function: Difference between revisions

Revision as of 00:41, 26 November 2005

Revision as of 01:49, 26 November 2005

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'''Characteristic function''' can refer to several distinct concepts:

* In one [[mathematics|mathematical]] usage, the '''characteristic function''' of a [[subset]] ''A'' of a [[set]] ''X'' is the [[indicator function]] <math>\chi_A: X \to \{0, 1\}</math> with ___domain ''X'' having value 1 at points of ''A'' and 0 at points of ''X''&nbsp;&minus;&nbsp;''A''.

* In one [[mathematics|mathematical]] usage, the '''characteristic function''' of a [[subset]] ''A'' of a [[set]] ''XS'' is the [[indicator function]] <math>\chi_A: XS \to \{0, 1\}</math> with ___domain ''XS'' havingwhich has value 1 at points of ''A'' and 0 at points of ''XS''&nbsp;&minus;&nbsp;''A''.

* In another mathematical usage, this one in [[probability theory]], the '''characteristic function''' of any [[probability distribution]] on the [[real number|real]] line is given by the following formula, where ''X'' is any [[random variable]] with the distribution in question: