The definition of \textit{sub-gaussian} from a book I work with is: $X\in\mathbb{R}^n$ is $(\Sigma,C)$ sub-gaussian if $$\mathbb{P}(\lvert X^\top u\rvert>t)<Ce^{-t^2/(2u^\top\Sigma u)}, \qquad u\in\mathbb{R}^n\setminus\{0\}, t>0.$$ And I wonder how I can show that $X\sim N(\mu,\Sigma)$ is $(\Sigma,C)$ sub-gaussian.
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$\begingroup$ What have you tried? $\endgroup$– AndrewCommented Nov 3, 2023 at 14:25
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$\begingroup$ I think I found the solution. $\endgroup$– T.I.Commented Nov 4, 2023 at 16:25
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