Support of Discrete Random Variable

Definition

Let

• $X$ : Discrete random variable
• $\mathcal{D}$ : Space of $X$

If

$${\mathcal{S}}_X=\{x\in \mathcal{D}:P(X=x)>0\}$$

Then we say ${\mathcal{S}}_X$ is the support of $X$

Remark

Interpretation

Notice that $P(X=x)$ must be positive. This means you can interpret support of $X$ as:

• The set where $P(X)$ is not $0$
• Set of all possible outcomes that can actually occur (have positive probability)