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Let $X_{1}$, $X_{2}$, $X_{3}$, $X_{4}$, $X_{5}$ and $X_{6}$ be real-valued random variables that have the same probability distribution with finite moments, and they are independent. Does anyone know how to apply Markov inequality to show that $$ P\left(X_{1}+X_{2}+X_{3}+X_{4}+X_{5}+X_{6}\le3\right)\le2P\left(X_{1}\le1\right)? $$

Thanks for any helpful answers!

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    All that's given is that the X's have the same distribution; however, we don't know if the first (absolute) moment of X exists, nor do we know whether the X's are independent. I fail to see how you can even apply Markov's inequality in this context.2012-09-24
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    Dear Mico, I have added the assumptions accordingly.2012-09-24
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    @h636: And you should not have.2012-09-24

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