# Markov's Inequality

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

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

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