GE 331-Lecture 19 - Probability Inequalities Markov...

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IE 300/GE 331 Lecture 19 Negar Kiyavash, UIUC 1 Probability Inequalities: Markov inequality: X is non-negative r.v., then for any a>0: Chebyshev inequality: If X is an r.v. with mean μ and variance σ 2, then Important trick: If we cannot calculate variance of a finite ranged r.v (it takes values in the range [a,b]), then we can use the bound V[X] <= (b-a) 2 /4 . ] [ ) ( P a X E a X . ) | (| P 2 2 c c X σ μ
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