Beta PDF
From CFD-Wiki
A 
probability density function depends on
two moments only; the mean 
and the variance 
.
This function is widely used in turbulent combustion to define the scalar distribution at each
computational point as a function of the mean and variance.
Assuming that the sample space of the scalar varies betwen 0 and 1.
The beta function PDF has the form
- Failed to parse (syntax error): P (\eta) = \frac{\eta^\{alpha-1} (1- \eta)^{\beta-1}}{\Gamma(\alpha) \Gamma(\beta)} \Gamma(\alpha + \beta)
where 
is the gamma function and the parameters
and are related through
where 
is
