Definition:Characteristic Function of Random Variable

Definition
Let $X$ be a random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.

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


 * $\map \phi t = \expect {e^{i t X} }$

where:
 * $i$ is the imaginary unit
 * $\expect \cdot$ denotes expectation.