Problem 7 (Gaussian Message Passing over Markov Random Field) Let's consider the belief propagation algorithm for Gaussian pairwise MRF, where the potentials are defined as following: t(xt)s,t=exp(21Attxt2+btxt)=exp(21xsAstxt) where A is the precision matrix and b is just a parameter. Our goal is to derive the message passed into node xt, i.e. m(xt). Part 1: To begin with, we need a fact that the product of two Gaussians is a scaled Gaussian. Show: N(x1,11)N(x2,21)=CN(x,1), solve for and , where C is a constant. Part 2: Solve for m(xt). Hint: First solve for the messages passed into Node t 's neighbor nodes from their neighbors excluding t, then use these messaged to represent m(xt). You can directly use this result if needed: exp(ax2+bx)dx=aexp(4ab2)