# Summing many non-standard i.i.d. uniform random variables

all!

I have looked up a fair bit on this question and learned much about the problem. But haven't been able to get any crisp answers. Sorry, if I'm missing something obvious.

I know one can use the Irwin-Hall Distribution to sum standard uniform random variables. However, I need to sum 100 i.i.d. Uniform[-1,1] random variables. So, Irwin-Hall cannot be applied- at least, not directly.

The ultimate goal is to calculate the probability that the absolute value of the sum of the hundred RVs exceeds 10.

Using the convolution method for 100 variables is extremely tedious. So, I didn't try that.

Any hints on how the distribution for the sum can be computed? I read somewhere that Irwin-Hall can be tweaked for [-1, 1] but have no idea how.

Can it be approximated by Normal Distribution, since n is quite large (100) and the mean and standard deviation for all the RVs are known?

Many thanks.

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Look up Central Limit Theorem. –  Dave S Oct 28 '13 at 11:28
Thanks. I did look it up, and do get that for a large n, the probability converges to the mean. But the question is whether 100 is large enough and how accurate the approximation will be, given I need to calculate the exact probability that the sum exceeds 10. –  Quester Oct 28 '13 at 12:11
I think Berry-Esseen theorem states something about the convergence rate to the normal distribution. –  Dave S Oct 28 '13 at 12:28