Independence

We say two variables are independent if knowing one provides no information about another.

Mathematically we say,

$f_{X,Y}(x,y)=f_X(x)f_Y(y)$ (1) holds if the variables are independent. Alternatively we may choose to factorize the joint pdf into marginal pdfs.

$$f_{Y\mid X}(y\mid x)=f_Y(y)(1)$$