Pairwise independence

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

Fact: For pairwise independent random variables $X_1,…,X_m$, $$\mathrm{Var}[X_1 + X_2 + ... + X_m] = \mathrm{Var}[X_1] + \mathrm{Var}[X_2] + ... + \mathrm{Var}[X_m]$$

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

Weaker than Mutual independence.

See Types of Independence.