Central Limit Theorem

  This theorem states that the sum of a large number of random variables is approximately normally distributed, even though the random variables themselves may follow any distribution or be taken from different distributions. The only conditions are that the original random variables must have finite expectation, variance and higher moments.

Although the theorem is only true of an infinite number of variables, in practice the convergence to the Gaussian distribution is very fast. For example, the distribution of the sum of ten uniformly distributed random variables is already indistinguishable by eye from an exact Gaussian (see [Grimmett92]).