The psi-2 norm of a Gaussian

NumericalIntermediate⏱ 15 minHigh-Dim Probabilityorliczgaussianpsi-2

Problem

Compute $\|X\|_{\psi_2}$ exactly for $X\sim\Ncal(0,\sigma^2)$ , where $\|X\|_{\psi_2}=\inf\{t>0:\E e^{X^2/t^2}\le2\}$ .

Compute the requested quantities and say what they mean. A number without an interpretation is not an answer.

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