2.31 ( ) Consider two multidimensional random vectors x and z having Gaussian distributions p(x) = N(x|x,x) and p(z) = N(z|z,z) respectively, together with their

2.31 ( ) Consider two multidimensional random vectors x and z having Gaussian distributions p(x) = N(x|μx,Σx) and p(z) = N(z|μz,Σz) respectively, together with their sum y = x+z. Use the results (2.109) and (2.110) to find an expression for the marginal distribution p(y) by considering the linear-Gaussian model comprising the product of the marginal distribution p(x) and the conditional distribution p(y|x).