Probability inequality

May 2010
12
0
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.
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e means epsilon
 
May 2009
301
34
You would probably use Chebyshev's Inequality.