Two real-valued or vector-valued random variables X, Y are independent for probability measure P (written: X ⊥ Y [P ]) if for all sets A and B, P[X ∈ A, Y ∈ B] = P[X ∈ A] · P[Y ∈ B]. For jointly discrete or jointly continuous random variables this is equivalent to factoring of the joint probability mass function or probability density function, respectively. The variables X and Y are conditiona...