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Mean = Most Probable Value - Statistical Mechanics

  1. Feb 15, 2012 #1
    Hey guys,

    In statistical mechanics I need to explain why the mean value is approximately equal to the most probable value for systems with a large number of random variables.

    Now I can provide an example of the binomial distribution and show what happens when N tends to infinity ( it goes to a dirac delta function), however I'm not sure how to explain why this happens exactly.

    I believe the basis is the Law of Large numbers, I'm not sure if stating this law is sufficient enough to though.

    Cheers for any help,
  2. jcsd
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