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Math Help - Probability inequality

  1. #1
    Newbie
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    Probability inequality

    How can I proceed for this question.
    Thanks.

    Let f=f(x) be a nonnegative even function that is non-decreasing for positive x, Then for a random X with |X(w)|<=C,

    {Ef(X)-f(e)}/f(C) < = P{|X-E(X)| > = e} <= {Ef(X-EX)}/f(e).

    In particular, if f(x)=x^2

    {E x^2-e^2}/C^2 < = P{|X-E(X)| > = e} <= V(X)/e^2.

    =========
    e means epsilon
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  2. #2
    Senior Member Sampras's Avatar
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    You would probably use Chebyshev's Inequality.
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