Let (U) be a UNIFORm ([0,1]) random variable and let (left{X_{n}ight}_{n=1}^{infty}) be a sequence of random variables

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Let $U$ be a UNIFORm $[0,1]$ random variable and let $\left\{X_{n}ight\}_{n=1}^{\infty}$ be a sequence of random variables such that

\[X_{n}=\delta\left\{U ;\left(0, \frac{1}{2}-[2(n+1)]^{-1}ight)ight\}+\delta\left\{U ;\left(\frac{1}{2}+[2(n+1)]^{-1}, 1ight)ight\}\]

for all $n \in \mathbb{N}$. Prove that $X_{n} \xrightarrow{\text { a.c. }} 1$ 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 (U) be a UNIFORm ([0,1]) random variable and let (left{X_{n}ight}_{n=1}^{infty}) be a sequence of random variables

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Introduction To Statistical Limit Theory

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