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Characteristic Function of a Gaussian Random Variable

Last updated Nov 1, 2022

# Statement

Suppose $(\Omega, \mathcal{M}, \mathbb{P})$ is a Probability Space and $X \sim \mathcal{N}(\mu, \sigma^{2})$. Then

$$\phi_{X}(t) = \exp (i t \mu - \frac{\sigma^{2} t^{2}}{2})$$

# Proof

# Other Outlinks