In probability theory, the general form of Bienaymé's identity, named for Irénée-Jules Bienaymé, states that
This can be simplified if are pairwise independent or just uncorrelated, integrable random variables, each with finite second moment. This simplification gives:
The above expression is sometimes referred to as Bienaymé's formula. Bienaymé's identity may be used in proving certain variants of the law of large numbers.
See also
Variance Propagation of error Markov chain central limit theorem Panjer recursion Inverse-variance weighting Donsker's theorem Paired difference test
References