Question: 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

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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