Exercise 1.5 Show that if Y is an r-dimensional random vector with Y N(,V) and if B is a fixed nr matrix, then BY

Exercise 1.5 Show that if Y is an r-dimensional random vector with Y ∼N(μ,V)

and if B is a fixed n×r matrix, then BY ∼ N(Bμ,BVB).

In linear model theory, Theorem 1.2.3 is often applied to establish independence of two linear transformations of the data vector Y.