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    Markov's Inequality

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    Let S be a random variable (not necessarily positive). Prove using Markov's inequality that for every p>0 and for every constant q,

    P(S>=a) (=<) exp(-pq)E(exp(pS))

    Here >= denoted greater than or equal to, and =< denotes less than or equal to.

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    Solution Preview

    Please see the attachment for solution. If you need any clarification about this problem please ask me. Thank you

    Note that since exp(x) is a non-negative monotonic increasing function if x>y then ...

    Solution Summary

    The solution contains the derivation of a probability inequality using Markov's inequality.