Bienaymé's identity - Alchetron, The Free Social Encyclopedia

In probability theory, Bienaymé's identity states that

Var ⁡ ( S n ) = ∑ k = 1 n Var ⁡ ( X k ) ,

where X 1 , … , X n are pairwise independent integrable random variables with second moments and S n = ∑ k = 1 n X k .

Bienaymé's identity may be used in proving certain variants of the law of large numbers.

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