Central Limit Theorem

see also:

• Gaussian Kernel

The Central Limit Theorem states that, under certain conditions, the sum (or average) of a large number of independent, identically distributed random variables, irrespective of the original distribution, will tend towards a normal (Gaussian) distribution as the number of variables increases. Mathematically, if $X_1,X_2,...,X_n$ are random variables with mean $\mu$ and variance ${\sigma }^2$, then the sum $\frac{1}{\sqrt{n}}{\sum }_{i=1}^n(X_i-\mu )$ converges in distribution to a normal distribution with mean $0$ and variance ${\sigma }^2$ as $n\to \infty$.