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fixed link, assumed "probability density function" was intended (rather than, say "probability density) |
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= \int_{-\infty}^{\infty} f_X(x)\, e^{itx}\,dx.</math>
Here ''t'' is a [[real number]], E denotes the [[expected value]] and ''F'' is the [[cumulative distribution function]]. The last form is valid only when the [[probability density function]] ''f'' exists. The form preceding it is a [[Riemann-Stieltjes integral]] and is valid regardless of whether a density function exists.
If ''X'' is a [[vector space|vector]]-valued random variable, one takes the argument ''t'' to be a vector and ''tX'' to be a [[dot product]].
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