Let (F(x)) be the distribution function of (xi). Prove that if (mathbf{M} xi) exists, then [ M

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Let $F(x)$ be the distribution function of $\xi$. Prove that if $\mathbf{M} \xi$ exists, then

\[ M \xi=\int_{0}^{\infty}[1-F(x)+F(-x)] d x \]

and for the existence of $\boldsymbol{M} \xi$ it is necessary that \[ \lim _{x \rightarrow-\infty} x F(x)=\lim _{x \rightarrow \infty} x[1--F(x)]=0 \]

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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)) be the distribution function of (xi). Prove that if (mathbf{M} xi) exists, then [ M

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Theory Of Probability

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