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Chebyshev's Inequality Problem!

  1. Nov 17, 2007 #1
    Let X be uniformly distributed over (-2,2). Use Chebyshev's inequality to estimate P(abs(x) >= 1) and compare to the exact value.

    The answer in the book got something different than what i got so i wanted to see if i was right

    EX of a uniformly distrubuted RV is (a+b)/2 so -2+2/0 =0
    So i plugged into the formula.

    P(abs(x)>=1 <= sigma^2

    the variance of a uniformly RV is (b-a)^2/12 so (2-(-2))^2=14 and 14/12 is 4/3.

    my first answer ======= P(abs(x)>=1 <= 4/3

    For the exact part I used the P(X<=x) cdf of a unform RV and got F(1)=3/4. So 1-F(1) = 0.25 which is the probability we are looking for.

    Did i do this right? Thanks!
  2. jcsd
  3. Nov 18, 2007 #2


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    Write out Cheb's Ineq. and walk through the steps.
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