3.8 ( ) www Consider the linear basis function model in Section 3.1, and suppose that we have already observed N data points, so that the posterior distribution over w is given by (3.49). This posterior can be regarded as the prior for the next observation.

By considering an additional data point (xN+1, tN+1), and by completing the square in the exponential, show that the resulting posterior distribution is again given by (3.49) but with SN replaced by SN+1 and mN replaced by mN+1.