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 and only 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 $\lambda \in \R$.