# Discrete Joint Distribution

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

Properties:

- $f(x,y)≥0$
- $∑_{x∈X}∑_{y∈Y}f(x,y)=1$

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 $P(x∩y)$

### Concepts

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