Definition:Sub-Gaussian Distribution

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Definition

The distribution of a random variable $X$ with expectation $\mu = \expect X$ is called sub-Gaussian if there exists a $\sigma \in \R_{>0}$ such that:

$\expect {e^{\lambda \paren {X - \mu} } } \le e^{\sigma^2 \lambda^2 / 2}$

for all $\lambda \in \R$.