Editing Central limit theorem (section)

==Extensions==

===Products of positive random variables===
The [[logarithm]] of a product is simply the sum of the logarithms of the factors.  Therefore, when the logarithm of a product of random variables that take only positive values approaches a normal distribution, the product itself approaches a [[log-normal distribution]].  Many physical quantities (especially mass or length, which are a matter of scale and cannot be negative) are the products of different [[random]] factors, so they follow a log-normal distribution.  This multiplicative version of the central limit theorem is sometimes called [[Gibrat's law]].

Whereas the central limit theorem for sums of random variables requires the condition of finite variance, the corresponding theorem for products requires the corresponding condition that the density function be square-integrable.<ref name=Rempala/>