Discrete Distributions

Abstract

The distribution of a random number X is said to be discrete if there is a finite or enumerable set $A\subset I(X)$ such that $\mathbf{P}(X\in A)=1$. This is obviously the case when I(X) is itself finite or enumerable, since in this case we may take $A=I(X)$. Let $A=\{x_1,x_2,\ldots \}$ and define $p(x_i)=\mathbf{P}(X=x_i)$.