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Sampling random numbers from a distribution

  1. Aug 23, 2008 #1
    Let's say we have a given probability distribution. We sample two random numbers from this distribution, say x1 and x2. What is the probability that x1 > x2? Is it always 0.5? Does it even depend on the distribution? Sorry if it appears trivial. I just can't seem to wrap my mind around this.


    Thanks!
     
  2. jcsd
  3. Aug 23, 2008 #2

    Ygggdrasil

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    Science Advisor

    Well, you can make the easy argument from symmetry. Since there is nothing special about picking x1 first and x2 second, P(x1>x2) = P(x1<x2). If we assume P(x1=x2) is negligible, clearly P(x1>x2) = P(x1<x2) = 0.5.
     
  4. Aug 24, 2008 #3

    statdad

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    Homework Helper

    It will always be [tex] 0.5 [/tex] as long as

    [tex]
    \Pr(X_1 = X_2) = 0
    [/tex]
     
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