Suppose G is nn non-negative definite, and is n1. (a) Find an n1 vector U of

Suppose G is n×n non-negative definite, and α is n×1.

(a) Find an n×1 vector U of normal random variables with mean 0 and cov(U ) = G. Hint: let V be an n×1 vector of independent N (0, 1) variables, and let U = G1/2V .

(b) How would you modify the construction to get E(U ) = α?