Multivariate Distributions

The following definition generalizes the concept of joint probability mass function of two

discrete random variables to n > 2 discrete random variables.

Definition Let X1, X2, . . . , Xn be discrete random variables defined on the same sam-

ple space, with sets of possible values A1, A2, . . . , An, respectively. The function

p(x1, x2, . . . , xn) = P (X1 = x1, X2 = x2, . . . , Xn = xn)

is called the joint probability mass function of X1, X2, . . . , Xn.