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Sum of Normal random numbers

  1. Feb 8, 2010 #1
    For random variables Xk~N(0,1) is there any way of representing the following sum by another random variable?
    lim_{n\rightarrow \infty}\sum_{k=0}^n X_k

  2. jcsd
  3. Feb 8, 2010 #2

    D H

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    What does the central limit theorem have to say about this question?
  4. Feb 8, 2010 #3
    Thanks DH for your reply, but I've already taken the CLT into consideration. However, since there is no normalizing factor (1/n) in front of the sum I didn't think it applied.

    Does it?
  5. Feb 8, 2010 #4


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    The random variable for sum to n is normal with a variance = n. The distribution function does not converge to anything as n -> ∞.
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