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Does anyone know how to start this question?

Let random vectors $x,u,v$ have joint Gaussian distribution, and $u,v$ be independent. Show that $E(x|u,v)=E(x|u)+E(x|v)-E(x)$.

  • 4
    Write $x=au+bv+w$ for some numbers $a$ and $b$, with $(u,v,w)$ gaussian and independent.2011-11-03
  • 0
    Are random vectors the same as random variables? or do $x,u,v$ all have multivariate jointly Gaussian distributions (that is, the components of each are not necessarily independent Gaussian random variables) but the joint distribution of $u$ and $v$ factors into the product of the _jointly_ Gaussian distributions of _vectors_ $u$ and of $v$?2011-11-03
  • 0
    "Are random vectors the same as random variables?" I really want to assume they are the same here.2011-11-04
  • 0
    A random vector is simply a vector-valued random variable.2011-11-04

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