Joint Probability Density Function

For Continuous Random Variable $X,Y$, describes the area of probability within a Region $B=[a,b]\times [c,d]\subset {\mathbb{R}}^2$ $P((X,Y)\in B)=\int {\int }_R{f}_{X,Y}(x,y)dxdy$

Properties

• $f_{X,Y}(x,y)\ge 0,\forall x,y\in \mathbb{R}$
• $\int {\int }_{{\mathbb{R}}^2}{f}_{X,Y}(x,y)dxdy=1$