Independent Random Variable

probability-theory

Definition

Independent Random Variable

Two random variables $X,Y$ re independent if knowing the outcome gives you absolutely no information about the outcome of the other.

• Discrete: $X\perp Y⟺P(X=x,Y=y)=P(X=x)\cdot P(Y=y)$
• Continuous: $X\perp Y⟺f_{X,Y}(x,y)=f_X(x)\cdot f_Y(y)$