In probability theory, the general[1] form of Bienaymé's identity states that
.
This can be simplified if are pairwise independent or just uncorrelated, integrable random variables, each with finite second moment.[2] 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.[3]