pairwise independence

Definition

$X_1,…,X_k$ are pairwise independent if $X_i,X_j$ are independent for all $i,j \in \{1,…,k\}$

Fact: For pairwise independent random variables $X_1,…,X_m$,

i.e. we require that for any $i,j$ that $X_i$ and $X_j$ are independent.

Notes

• Weaker than mutual independence.
• See types of independence.