Exercise 3.17 Let X and Z be statistically independent Gaussian rvs of arbitrary dimension n and m respectively. Let Y = [H]X + Z, where [H] is an arbitrary real n X m matrix. (a) Explain why X1, . .., Xn, ZI, ..., Zm must be jointly Gaussian rv s. Then explain why X1, .. ., Xn, Yl, . .., Ym must be jointly Gaussian. (b) Show that if [Kx] and [Kz] are non-singular, then the combined covariance matrix [K] for (X1, . . ., Xn, Y1,.. ., Ym) must be non-singular