Definition:Independent Random Variables/Discrete/Pairwise Independent

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Definition

Let $\EE$ be an experiment with probability space $\struct {\Omega, \Sigma, \Pr}$.

Let $X = \tuple {X_1, X_2, \ldots, X_n}$ be an ordered tuple of discrete random variables.

Then $X$ is pairwise independent if and only if $X_i$ and $X_j$ are independent (of each other) whenever $i \ne j$.

Sources

• 1986: Geoffrey Grimmett and Dominic Welsh: Probability: An Introduction ... (previous) ... (next): $\S 3.3$: Independence of discrete random variables