Joint Probability Mass Function

Describes the probability of two Discrete RV being exactly equal to two values.

Definition

$p_{X,Y}(x,y)=P(X=x,Y=y)=P(\{X=x\}\cap \{Y=y\})$

Properties

• $p_{X,Y}(x,y)\ge 0,\forall x,y$
• ${\sum }_{x,y}{p}_{X,Y}(x,y)=1$