2.27 () Let x and z be two independent random vectors, so that p(x, z) = p(x)p(z).

Show that the mean of their sum y = x+z is given by the sum of the means of each of the variable separately. Similarly, show that the covariance matrix of y is given by the sum of the covariance matrices of x and z. Confirm that this result agrees with that of Exercise 1.10.