For any random variable X for which EX2 and E|X| exist, show that P(|X| > 6) does

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For any random variable X for which EX2 and E|X| exist, show that P(|X| > 6) does not exceed either EX2/b2 or E|X|/6, where b is a positive constant. If f(x) = e~x for x > 0, show that one bound is better when b = 3 and the other when b = √2. (Notice Markov's Inequality in Miscellanea 3.8.2.)
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Statistical Inference

ISBN: 978-0534243128

2nd edition

Authors: George Casella, Roger L. Berger

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