In probability theory, a pairwise independent collection of random variables is a set of random variables any two of which are independent. Any collection of mutually independent random variables is pairwise independent, but some pairwise independent collections are not mutually independent. Pairwise independent random variables with finite variance are uncorrelated.

A pair of random variables X and Y are independent if and only if the random vector (X, Y) with joint cumulative distribution function (CDF) ${\displaystyle F_{X,Y}(x,y)}$ satisfies

${\displaystyle F_{X,Y}(x,y)=F_{X}(x)F_{Y}(y),}$

or equivalently, their joint density ${\displaystyle f_{X,Y}(x,y)}$ satisfies

${\displaystyle f_{X,Y}(x,y)=f_{X}(x)f_{Y}(y).}$

That is, the joint distribution is equal to the product of the marginal distributions.

Unless it is not clear in context, in practice the modifier "mutual" is usually dropped so that independence means mutual independence. A statement such as " X, Y, Z are independent random variables" means that X, Y, Z are mutually independent.