6. Suppose Y = (Y₁, Y2, Y3)' ~ N(μ, Σ) where E) (a) (b) f [2 1 11 and Σ = |1 3 0 10 2 Find the joint distribution of Z₁ = Y₁+Y₂+ Y3 and Z₂ = Y₁ - Y₂. Find the distribution of given Y₁ = 1/2

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6. Suppose Y = (Y₁, Y2, Y3)' ~ N(μ, E) where
(a)
(b)
μ = 1
-
[21 11
and Σ = |1 3 0
101
Find the joint distribution of Z₁ = Y₁+Y₂+ Y3 and Z₂ = Y₁ - Y₂.
Find the distribution of
Y₁
Y₂
given Y3 =
1
2
Transcribed Image Text:6. Suppose Y = (Y₁, Y2, Y3)' ~ N(μ, E) where (a) (b) μ = 1 - [21 11 and Σ = |1 3 0 101 Find the joint distribution of Z₁ = Y₁+Y₂+ Y3 and Z₂ = Y₁ - Y₂. Find the distribution of Y₁ Y₂ given Y3 = 1 2
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