Central limit theorem
The Central limit theorem states that the sum of a sufficiently large number of independent random variables tends toward a Normal random variable, independently of the distributions of the random variables which are added. A consequence of this theorem is this: the sample mean (normalized sum of realizations of a random variable) is another random variable, which probability density function tends to be Gaussian if the number or samples is large enough.
A condition to this theorem is that the variance of the added independent random variables must tend to infinity when this number also tends to infinity.
Figure 5 Probability density function of the sum of independent uniform random variables
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- Digital Connections, Scotland
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