Characteristic Function of a Gaussian Random Variable
# Statement
Suppose $(\Omega, \mathcal{M}, \mathbb{P})$ is a Probability Space and $X \sim \mathcal{N}(\mu, \sigma^{2})$. Then
$$\phi_{X}(t) = \exp (i t \mu - \frac{\sigma^{2} t^{2}}{2})$$
Search
Suppose $(\Omega, \mathcal{M}, \mathbb{P})$ is a Probability Space and $X \sim \mathcal{N}(\mu, \sigma^{2})$. Then
$$\phi_{X}(t) = \exp (i t \mu - \frac{\sigma^{2} t^{2}}{2})$$