Let (left{X_{n}ight}_{n=1}^{infty}) be a sequence of random variables. Suppose that for every (varepsilon>0) we have that [limsup

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Let $\left\{X_{n}ight\}_{n=1}^{\infty}$ be a sequence of random variables. Suppose that for every $\varepsilon>0$ we have that

\[\limsup _{n ightarrow \infty} P\left(\left|X_{n}ight|>\varepsilonight) \leq c \varepsilon\]

where $c$ is a finite real constant. Prove that $X_{n} \xrightarrow{p} 0$ as $n ightarrow \infty$.

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Introduction To Statistical Limit Theory

ISBN: 9780367383138

1st Edition

Authors: Alan M. Polansky

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Question Posted: Mar 15, 2024 02:00 AM

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Let (left{X_{n}ight}_{n=1}^{infty}) be a sequence of random variables. Suppose that for every (varepsilon>0) we have that [limsup

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Introduction To Statistical Limit Theory

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