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Mark viking (talk | contribs) Removed "The most common and universal usage"; I don't thank any one of these uses of the term is dominant or universal; added ROC |
m math formulae, punctuation, no boldface here |
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* As a synonym for [[indicator function]], that is the function
::<math>\mathbf{1}_A
:which for a given subset ''A'' of ''X'', has value 1 at points of ''A'' and 0 at points of ''X'' − ''A''.
* In probability theory, the [[characteristic function (probability theory) | characteristic function]] of any probability distribution on the real line is given by the following formula, where ''X'' is any random variable with the distribution in question:
▲::<math>\varphi_X(t) = \operatorname{E}\left(e^{itX}\right)\,</math>
▲:where '''E''' means expected value. This concept extends to multivariate distributions.
* The [[characteristic function (convex analysis) | characteristic function]] in convex analysis:
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