Characteristic Function
- $X: \Omega \rightarrow \mathbb{R}$
- r.v.
Characteristic function of $X$ is defined by
\[\begin{eqnarray} \phi_{X}(t) & := & \mathrm{E} \left[ e^{-i t X} \right] . \end{eqnarray}\]Characteristic function of $X$ is defined by
\[\begin{eqnarray} \phi_{X}(t) & := & \mathrm{E} \left[ e^{-i t X} \right] . \end{eqnarray}\]