Normal distribution

From WilmottWiki

The Normal distribution is a probability continuous distribution, unbounded below and above, and is symmetrical about its mean. It has two parameters: $a$ , location; $b>0$ scale. Its probability density function is given by

$\frac{1}{\sqrt{2\pi}\;b}e^{-\frac{(x-a)^2}{2b^2}}$ .

This distribution is commonly used to model equity returns, and, indeed, the changes in many financial quantities. Errors in observations of real phenomena are often normally distributed. The normal distribution is also common because of the Central Limit Theorem.

Mean = $a$ and Variance = $b^2$ .