Problem III. Linear Regression $(10$ points$)$

Consider $y=w^T(x)+v,$ where $v$ is Gaussian, i$.$e$.,(0,{}^{-1}|),$ and $w$ has a Gaussian priori, i$.$e$.,(m_0,{}^{-1}I|).$ Assume that $(x)$ is known, please derive the posterior distribution, $(D,,m_0,|),$ the posterior predictive distribution, $((hat(x)),D,,m_0,|),$ and the prior predictive distribution, $(,m_0,|),$ respectively, where $D=\{{}_n,y_n\},n=1,$dots,$N,$ is the training data set and ${}_n=(x_n).$