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Hoeffding to bound Orlicz norm

As I understand these notations, $\Psi_2(x)=\exp(x^2)-1$ and $\|Z\|_{\Psi}=\inf \{c>0 : \mathbb{E} (\Psi(|Z| / c)) \leqslant 1\}$. So the inequality $\|Z\|_{\Psi}\leqslant c$ means that $\mathbb{E} …
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