Definition:Characteristic Function of Random Variable

Definition
Let $X$ be a random variable on a probability space $\left({\Omega, \Sigma, \Pr}\right)$.

The characteristic function of $X$ is the mapping $\phi: \R \to \C$ defined by:


 * $\phi \left({t}\right) := \mathop{\mathbb E} \left[{e^{i t X}}\right]$

where:
 * $i = \sqrt{-1}$
 * $\mathbb E$ is the operator for expectation.