slides_5_conddist

# 64 ∙ without specifying the full distribution of u

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Unformatted text preview: 64 ∙ Without specifying the full distribution of U we cannot know the full conditional distribution, D Y | X . But at least we know the mean and variance (if we know , , and U 2 ). ∙ All of the findings for variances values of linear combinations of vectors have extensions to conditional variances. 65 ( cv5 ) If A x is an r m function and b x and m 1 function then Var A X Y b X | X A X Var Y | X A X ′ ∙ As a special case, Var a X ′ Y b X | X a X ′ Var Y | X a X where a X is an m 1 vector. We can write this out as Var a 1 X Y 1 a 2 X Y 2 ... a m X Y m b X | X ∑ i 1 m a i X 2 Var Y i | X 2 ∑ i 1 m − 1 ∑ j i 1 m a i X a j X Cov Y i , Y j | X 66 ∙ If Cov Y i , Y j | X 0, all i ≠ j then Var ∑ i 1 m a i X Y i X ∑ i 1 m a i X 2 Var Y i | X ∙ As a special case of this, with a i X ≡ 1, Var ∑ i 1 m Y i X ∑ i 1 m Var Y i | X just like in the case of unconditional variances. 67...
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64 ∙ Without specifying the full distribution of U we...

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