Question

1. Let x ∼ Np(µ, Σ). (1) Find the distribution of xp conditional on x1, ....

1. Let x ∼ Np(µ, Σ).
(1) Find the distribution of xp conditional on x1, . . . , xp−1.
(2) Suppose Σ =(1 ρ ρ 1 )and let y1 = x1 + x2 and y2 = −x1 + x2. Determine
the joint distribution of y1 and y2.
(3) Suppose Σ =( σ11 σ12 σ21 σ22 )and define y1 and y2 as in part (2).Determine the joint distribution of y1 and y2.

Determine the conditional distribution y2 given y1.

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