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Stat - Upperbound on the probability that one random variable is greater than another

  1. Mar 6, 2010 #1
    1. The problem statement, all variables and given/known data

    I have two random variables with two corresponding means and standard deviations. I need to calculate the upperbound that one of the random variables is greater than the other. Any ideas I'm stumped?

    2. Relevant equations

    I've used the Markov inequality to calculate the upperbound that a random variable is greater than some given number, but I'm not sure if I can use it here or if I can how to do so.

    3. The attempt at a solution


    P(B - A > 0) <= [E(B) - E(A)] / 0

    but this obviously doesn't work. Could it be possible somehow to get the result by subtracting the different means and standard deviations using the Chebyshev inequality?


    P(|B-A|>r) <= (san dev)^2 / r^2

    but again r would equal 0.

    Thanks for any help you can give!
  2. jcsd
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