Let Zn, n 1, be a sequence of random variables and c a constant such that, for each 0, P Zn c 0 as n Show that, for any bounded continuous function g, E g(Zn) g(c) as n ...

For 0 let 0 be such that gx gc whenever x c Also let B be such t ...

Let Zn, n 1, be a sequence of random variables and c a constant such that,

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Let Zn, n ≥ 1, be a sequence of random variables and c a constant such that, for each ε > 0, P{|Zn − c| > ε}→0 as n→∞. Show that, for any bounded continuous function g,
E[g(Zn)]→g(c) as n→∞

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A First Course In Probability

ISBN: 9789332519077

9th Edition

Authors: Sheldon Ross

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Question Posted: Oct 22, 2015 03:05 AM

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Let Zn, n 1, be a sequence of random variables and c a constant such that,

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