Problem II$.$ Linear Gaussian System $(10$ points$)$

Consider $Y=Ax+V,$ where $x$ and $V$ are Gaussian, $(m_0,{}_0(0,{}^{-1}I|)|).$

What are the conditional distribution, $(x|),$ the joint distribution $p(Y,x),$ the marginal distribution, $p(Y),$ the posterior distribution, $|)=(y,,m_0,{}_0,$ the posterior predictive distribution, $|)=(y,,m_0,{}_0,$ and the prior predictive distribution, $(,m_0,{}_0|),$ respectively?