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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

 P( intersection _(i=1)^nA_i)=product_(i=1)^nP(A_i).
(3)

Statistically independent variables are always uncorrelated, but the converse is not necessarily true.


See also

Bayes' Theorem, Conditional Probability, Independent Events, Independence Complement Theorem, Uncorrelated

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Cite this as:

Weisstein, Eric W. "Independent Statistics." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/IndependentStatistics.html

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