Bienaymé's identity
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]
See also
- Variance
- Propagation of error
- Markov chain central limit theorem
- Panjer recursion
References
- .
- ISBN 3-540-90210-4.
- ISBN 0 521 26960 1.