# Sum of Normal random numbers

1. Feb 8, 2010

### Apteronotus

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

thanks

2. Feb 8, 2010

### D H

Staff Emeritus

3. Feb 8, 2010

### Apteronotus

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?

4. Feb 8, 2010

### mathman

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