Probability Mass Function (pmf)

Definition

Let

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

If $p_X(x)=P[X=x],\forall x\in \mathcal{D}$

Then we say that $p_X(x)$ is the probability mass function (pmf) of $X$

Properties of pmfs

Note that pmfs satisfies the following properties:

1. $0\le p_X(x)\le 1,\forall x\in \mathcal{D}$
2. ${\sum }_{x\in \mathcal{D}}{p}_X(x)=1$