4. Gaussian posterior distribution and marginal likelihood. Consider one random variable X that is Gaussian distributed with unknown mean μ and known variance o² = 1. X❘μ~N(1) The prior of μ is a standard Gaussian distribution: ~N(0, 1) EXERCISE: Compute the posterior and the marginal distribution of X. HINTS: Recall the PDF of a Gaussian distribution with mean and variance σ²: 1 p(x)= expl (エール √2π σ 02 and that the density fulfills: 1 1 p(x) xx exp{- μ 2 02 +1.x} (x € R) Recall that this implies that a random variable X whose PDF fulfills: 1 p(x) x exp{-ax² + bx} must have a N() distribution.