Discrete Joint Distribution

The joint pmf of discrete random variables $X$ and $Y$ is $f(x,y)=P(X=x,Y=y)$ where $x\in$ support of $X$ and $y\in$ support of $Y$

Properties:

1. $f(x,y)\ge 0$
2. ${\sum }_{x\in X}{\sum }_{y\in Y}f(x,y)=1$

Given that random variables are independent, we find that $f(x,y)=f_x(x)f_y(y)$.

For example, see the following:

Serendipity ahh this is where notation, it’s the same as saying $P(x,y)$, I was saying it mean the same as $P(x\cap y)$

Concepts

• Covariance
• Correlation

The joint distribution can be specified in terms of Conditional Probability.

Related

• Marginal Distribution