Normalisation Axiom (Probability Mass Function)

probability-theory

Definition

Normalisation Axiom

Let $p:\mathcal{X}\to \mathbb{R}$ be a candidate probability mass function. The normalisation axiom requires

$$\sum _{x\in \mathcal{X}}p(x)=1.$$

Thus the total probability mass distributed across all possible values is exactly one. Together with non-negativity, this is a defining axiom of a probability mass function.