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Central limit theorem

  1. Oct 5, 2009 #1
    1. The problem statement, all variables and given/known data
    consider an experiment with 2 possible outcomes, 1 and 0, with a priori probabilities p and
    1-p. we would like to find out the average (expected) deviation after N trials, of the relative frequency of the "1"s, N1/N
    Use the central limit theorem to find expected deviation.


    2. Relevant equations

    N1=[tex]\sum[/tex][tex]^{N}_{i=1}[/tex] ni , where ni is the outcome of the ith trial
    3. The attempt at a solution

    I know expected deviation of N1 is the square root of its variance.
    and variance is:
    [tex]\sigma[/tex][tex]^{2}[/tex]=<x[tex]^{2}[/tex]> - <x>[tex]^{2}[/tex]

    <x>=[tex]\sum[/tex][tex]^{N}_{i=1}[/tex]pi xi

    but i have to use central limit theorem
    [tex]\lim_{N \rightarrow inf } \left(N1/N)[/tex]

    and i'm lost , the question looks so easy but i have no idea what to do?
     
  2. jcsd
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