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Sum of IID random variables and MGF of normal distribution

  1. Dec 29, 2013 #1
    If the distribution of a sum of N iid random variables tends to the normal distribution as n tends to infinity, shouldn't the MGF of all random variables raised to the Nth power tend to the MGF of the normal distribution?

    I tried to do this with the sum of bernouli variables and exponential variables and didn'treally get anywhere with either.

    Does anyone know if this is even possible and where I can find the proof steps?
  2. jcsd
  3. Dec 29, 2013 #2

    Stephen Tashi

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    Science Advisor

    You have to specify what type of convergence you're talking about when you say "tends". ( http://en.wikipedia.org/wiki/Convergence_of_random_variables)

    The sum of iid random variables doesn't converge (in distribution) to a normal distribution. It's the mean of the sum that converges to a normal distribution.
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