I was wondering if anyone could help me with this (non-homework) question that I've been wondering about:

If you sum x integers in the interval [-y, y] z times, what is the expected standard deviation of the results you obtain?

For example, one trial would look like (Mathematica code):

Code: Select all

`(* numSum=x, interval=y, tries=z *)`

onTrial[numSum_, interval_, tries_] :=

StandardDeviation@

Table[ Total@RandomInteger[{-interval, interval}, numSum], {q, 1,

tries}];

Through brute force simulations, I arrived at the solution [math]\sigma \approx 0.579 \sqrt{x}y[/math]

However, I'm not positive that's right and it certainly isn't mathematically exact.

Could someone please help me find the answer mathematically?

Thanks,