Let be random variables all defined on the same probability space. The joint discrete density function of , denoted by , is the following function:
As in the single variable case, sometimes it's expressed as to mark the difference between this function and the continuous joint density function.
Also, as in the case where , this function satisfies:
In this case, .
![$ f_{X_1, X_2, ..., X_n}(x_1,x_2,...,x_n) = P[X_1 = x_1, X_2 = x_2, ... , X_n = x_n]$](http://images.planetmath.org:8080/cache/objects/573/l2h/img6.png "$ f_{X_1, X_2, ..., X_n}(x_1,x_2,...,x_n) = P[X_1 = x_1, X_2 = x_2, ... , X_n = x_n]$"){kind=small}
![$ f_{X_1, X_2, ..., X_n}(x_1,...,x_n) = P[ X_1 = x_1, X_2 = x_2, ... , X_n = x_n ]$](http://images.planetmath.org:8080/cache/objects/573/l2h/img12.png "$ f_{X_1, X_2, ..., X_n}(x_1,...,x_n) = P[ X_1 = x_1, X_2 = x_2, ... , X_n = x_n ]$"){kind=small}