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I always wanting to looking into harder random variable/probability/stochastic process/statistics books that are harder than the intro one and have multiple random variable but easy enough to have include this inequality which is multiple-variable Chebyshev's inequality

$P\left[ \sum_{ i = 1 }^n \frac{ ( X_i - \mu_i )^2 }{ \sigma_i^2 t_i^2 } \ge k^2 \right] \le \frac{ 1 }{ k^2 } \sum_{ i = 1 }^n \frac{ 1 }{ t_i^2 }$

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I am not sure if it has the problem you mention as I don't have my copy handy, but you might want to check out "Probability, Random Variables, and Stochastic Processes" by A. Papoulis. It is used in many graduate schools. –  Amzoti Mar 7 '13 at 1:46
    
There is nothing "multiple variable" about the inequality you give. It's a direct application of the standard Markov's inequality. If you can clarify what your question is (e.g., to know what harder means we need to know what you're already looking at. Also, what do you consider intro?) and add a little more detail, I think it would help. –  cardinal Mar 9 '13 at 15:39
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I THINK, THIS COULD BE USEFUL FOR YOU

SEE THIS ALSO, BY Dr. D.N. LAL

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$\large \textbf{PLEASE DON'T YELL!!}$ –  Arthur Fischer Mar 9 '13 at 15:32
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