A marginal distribution is the statistical distribution of one component or a subset of the components of a random
vector, without conditioning on the remaining components. If 
has joint probability
density function 
, then the marginal probability
density function of 
is
 |
The function 
is also called the marginal density. For discrete random
variables, the corresponding marginal probability mass function is obtained by
summing the joint probabilities over the unwanted component.
Marginalization preserves all probabilities involving only the retained components, but it generally discards information about their dependence on the components that were integrated or summed out.
