Independent Statistics
Two variates A and B are statistically independent iff the conditional probability P(A|B) of A given B satisfies
| P(A|B)=P(A), |
(1)
|
in which case the probability of A and B is just
| P(AB)=P(A intersection B)=P(A)P(B). |
(2)
|
If n events A_1, A_2, ..., A_n are independent, then
Statistically independent variables are always uncorrelated, but the converse is not necessarily true.
See also
Bayes' Theorem, Conditional Probability, Independent Events, Independence Complement Theorem, UncorrelatedExplore with Wolfram|Alpha
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Cite this as:
Weisstein, Eric W. "Independent Statistics." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/IndependentStatistics.html