Suppose U ∼ N(µ u ,V u ). Let Use equation 3.32 to show that u 1 and u 2 are independent if V 12 = 0. That is, if u is multivariate normal, then u 1 and u 2 uncorrelated implies u 1 and u 2 are...

Suppose U ∼ N(µ_u,V_u). Let

Use equation 3.32 to show that u₁
and u₂
are independent if V₁₂
= 0. That is, if u is multivariate normal, then u₁
and u₂
uncorrelated implies u₁
and u₂
are independent. (The joint density of u₁
and u₂
is the product of the marginal densities of u₁
and u₂, if and only if u₁
and u₂
are independent.)