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Comparing distributions

  1. Dec 4, 2013 #1
    Forgive me if this is a silly question, but here goes:

    Say you have two unrelated distributions (A and B) with known means and standard deviations. How would you determine the probability of any single value of A being greater than any single value of B?

    The easiest example I can come up with for clarification would be something like this:

    Over 1000 games baseball team A scores: μA=5 runs, σA=1 runs per game.
    Over 1000 games baseball team B scores: μB=4 runs, σB=2 runs per game.

    What is the probability on any given day that Team A outscored Team B? Sorry if this example seems elementary, but I am far from a statistician. Thanks for the help.
  2. jcsd
  3. Dec 4, 2013 #2


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    Science Advisor

    Direct method: Let C = A-B (there are standard methods to get the distribution function for C, given the distribution functions for A and B). Then compute P(C > 0).
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