Conditional Probability Density Function

A probability density function for Continuous RV $X,Y$ defined as: $f_{X|Y}(x|y)=\frac{f_{X,Y(x,y)}}{f_Y(y)}$

Properties

• Conditional PDF is a proper PDF
• $f_{X|Y}(x|y)={\int }_A{f}_{X|Y}(x|Y)dx,\forall A\subset \mathbb{R}$
• $f_{X,Y}(x,y)=f_X(x)f_{Y|X}(y|x),\forall x,y$ (Multiplication Rule of Probability)