Lemma 5.3.6 in this page states that:
$$\textrm{cov}(X+Y,Z)=\textrm{cov}(X,Z)+\textrm{cov}(Y,Z)$$
Does this property require that X, Y and Z must be pairwise independent?
2026-03-30 02:05:49.1774836349
Does this property of covariance require independence between random variables?
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$$cov (X+Y,Z)=E((X+Y)Z)-(E(X+Y))(EZ)$$ $$=EXZ+EYZ-EXEZ-EYEZ=cov (X,Z)+cov (Y+Z).$$ So this identity is always true. Inependence is not required.