Uniform sum distribution.

Hi,

I have a problem with calculating sum of n uniform variables on the interval [0,1].

I found solution here:

Uniform Sum Distribution -- from Wolfram MathWorld

I was thinking about charakteristic function but I do not understand one line:

Assume we calculated characteristic function of that sum and we obtained $\displaystyle (\frac{i(1-e^{i t})}{t})^n$.

Then we want to calculate probability density ( using $\displaystyle P(x)= \frac{1}{2 \Pi} \int_{- \infty}^ {\infty} e^{- i t x } \phi(t) dt$

But I do not know how calculate: $\displaystyle P(x)= \frac{1}{2 \Pi} \int_{- \infty}^ {\infty} e^{- i t x } (\frac{i(1-e^{i t})}{t})^n dt$

Please give me a hint :)

Re: Uniform sum distribution.

If the integer n is greater than 3, then you may safely invoke the Central limit theorem and claim that the exact probability distribution of the sum resembles a certain normal probability distribution; if you want to investigate the rate of convergence to the normal distribution, I suggest taking a look at the Berry-Essén theorem.