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Question: i 5 points let x be a random variable with...

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I. (5 points) Let X be a random variable with moment generating function M(t) = E [etx]. For t > 0 and a 〉 0, prove that and consequently, P(X > a inf etaM(t). t>0 These bounds are known as Chernoffs bounds. (Hint: Define Z etX and use Markov inequality.)

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