Let (f(x)>0) be a nondecreasing function. Prove that if (mathbf{M}(f(|xi-M xi|)) exists, then [ mathbf{P}{|xi-mathbf{M} xi| geqslant

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Let $f(x)>0$ be a nondecreasing function. Prove that if $\mathbf{M}(f(|\xi-M \xi|)$ exists, then

\[ \mathbf{P}\{|\xi-\mathbf{M} \xi| \geqslant \varepsilon\} \leqslant \frac{\mathbf{M} f(|\xi-\mathbf{M} \xi|)}{f(\varepsilon)} \]

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Theory Of Probability

ISBN: 9781351408585

6th Edition

Authors: Boris V Gnedenko

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Question Posted: May 06, 2024 04:02 AM

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Let (f(x)>0) be a nondecreasing function. Prove that if (mathbf{M}(f(|xi-M xi|)) exists, then [ mathbf{P}{|xi-mathbf{M} xi| geqslant

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Theory Of Probability

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