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Math Help - Convergence in distribution

  1. #1
    Julia B.
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    Convergence in distribution

    Help me please to solve my homework.
    Let X1,X2,...Xn be independent random variables such that P(Xk = k) = P(Xk = -k) = 1/(2k^2) and
    P(Xk = 1) = P(Xk = -1) = 1/2(1-1/k^2).
    Let Sn=∑Xk (k goes from 1 to n).
    Prove, that (1/√n)Sn converges in distribution to N(0,1) and var((1/√n)Sn) converges to 2. (n goes to infinity) Thanks;o)
    Julia
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  2. #2
    hpe
    hpe is offline
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    Quote Originally Posted by Julia B.
    Prove, that (1/√n)Sn converges in distribution to N(0,1) and var((1/√n)Sn) converges to 2. (n goes to infinity) Thanks;o)
    Julia
    Use the Fourier transform.
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