Density Function of a Random Vector

Topics: Probability - Random Vector - Density Function

---

(definition)

Let $X,Y$ be random variables.

We define the (joint) density function of the random vector $(X,Y)$ as:

$$f_{(X,Y)}(x,y)=\{\begin{array}{ll}\mathbb{P}(X=x,Y=y)& \text{if }(x,y)\in R_{(X,Y)}\\ 0& \text{otherwise}\end{array}$$