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Probability: Markov's and Cheyshev's Inequality what in the world?

  1. Oct 24, 2011 #1
    1. The problem statement, all variables and given/known data

    So these were introduced in my lecture and I'm not really clear what they do or why it's true or when they're useful. Can you please explain them to me in a simple way? Thank you.

    2. Relevant equations

    Markov's Inequality:
    If X is a non-negative random variable, (that is, P(X >= 0) = 1), then for any a > 0,
    P(X >= a) <= E(X) / a
    or equivalently,
    E(X) >= aP(X >= a)

    Chebyshev's Inequality:
    If s^2 = Var(X) and m = E(X) then for any k > 0,
    P(|X-m| >= ks) <= 1 / k^2
    or equivalently, for any a > 0,
    P((X-m)^2 >= a) <= s^2 / a
    (Just let a = k^2s^2 in the first form above.)

    3. The attempt at a solution

    I don't get it.
  2. jcsd
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