## Quick Reference

In a finite mixture model the distribution of the random variable *X* has a known form (e.g. normal), but the values of the parameters of the distribution are not known. Instead, it is known that the vector of the parameters takes one of the values *θ*_{1}, *θ*_{2},…, *θ** _{m}* with associated probabilities

*w*

_{1},

*w*

_{2},…,

*w*

*. If, for a continuous random variable, the probability density function of the*

_{m}*k*th of the possible distributions is denoted by f(

*x*,

*θ*

*), then the finite mixture distribution of*

_{k}*X*is given by . An equivalent result holds for a discrete random variable.

*Subjects:*
Probability and Statistics.