Non-negativity Axiom (Probability Mass Function)

probability-theory

Definition

Non-negativity Axiom

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

$$\forall x\in \mathcal{X}:p(x)\ge 0.$$

No possible value may carry negative probability mass. Together with normalisation, this is a defining axiom of a probability mass function.