2-8 MAP with Gaussian prior – vector version. Given z =x+w, where all the variables are n-vectors, with w \sim \mathcal{N}^{\prime}(0, P) \quad x \sim \mathcal{N}\left(\bar{x}, P_{0}\right) and x independent

of w. Find the MAP estimator of r in terms of z and the covariance of this estimator.