Exercise 1.5.2 Let Y = (y1, y2, y3) with Y N(, V ), where

Exercise 1.5.2 Let Y = (y1, y2, y3)

 with Y ∼ N(μ, V ), where

μ = (5, 6, 7)



and V =

⎡

⎣

2 0 1 0 3 2 1 2 4

⎤

⎦.

Find

(a) the marginal distribution of y1,

(b) the joint distribution of y1 and y2,

(c) the conditional distribution of y3 given y1 = u1 and y2 = u2,

(d) the conditional distribution of y3 given y1 = u1,

(e) the conditional distribution of y1 and y2 given y3 = u3,

(f) the correlations ρ12, ρ13, ρ23,

(g) the distribution of Z =



2 1 0 1 1 1

Y +



−15

−18

,

(h) the characteristic functions of Y and Z.