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Algebraist (talk | contribs) rm quote that doesn't seem to add much; disambig pages shouldn't have extraneous stuff |
Algebraist (talk | contribs) m move probability example up, since I think it and indicator function are the most common meanings |
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* The most common and universal usage is as a synonym for [[indicator function]], that is the function
::<math>\mathbf{1}_A: X \to \{0, 1\}</math>
:which for every subset ''A'' of ''X'', has value 1 at points of ''A'' and 0 at points of ''X'' − ''A''.
* The [[characteristic function (convex analysis)]] in convex analysis:▼
::<math>\chi_{A} (x) := \begin{cases} 0, & x \in A; \\ + \infty, & x \not \in A. \end{cases}</math>▼
* The [[characteristic state function]] in statistical mechanics.▼
* In probability theory, the [[characteristic function (probability theory)]] 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:
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:where '''E''' means expected value. This concept extends to multivariate distributions.
▲* The [[characteristic function (convex analysis)]] in convex analysis:
▲::<math>\chi_{A} (x) := \begin{cases} 0, & x \in A; \\ + \infty, & x \not \in A. \end{cases}</math>
▲* The [[characteristic state function]] in statistical mechanics.
* The [[characteristic polynomial]] in linear algebra.
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