Characteristic function: Difference between revisions

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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:

* ''&phi;:<math>\varphi(t) = E\left(e<sup>^{itX}\right).</supmath>)''.

If ''X'' is a [[vector]]-valued random variable, one takes the argument ''t'' to be a vector and ''tX'' to be a [[dot product]].