Two variates and are statistically independent Iff the Conditional Probability of given satisfies
(1)
in which case the probability of and is just
(2)
Similarly, events , , ..., are independent Iff
(3)
Statistically independent variables are always Uncorrelated, but the converse is not necessarily true.See also Bayes' Formula, Conditional Probability, Independence Complement Theorem, Uncorrelated