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?