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:which for every 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>
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:where '''E''' means expected value. This concept extends to multivariate distributions.
* The [[characteristic function (convex analysis) | characteristic function]] in convex analysis:
::<math>\chi_{A} (x) := \begin{cases} 0, & x \in A; \\ + \infty, & x \not \in A. \end{cases}</math>
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