Assuming (boldsymbol{Sigma}_{c}=mathbf{I}) for all classes, compute the posterior density (pleft(boldsymbol{mu}_{c} mid mathbf{X}^{c} ight)) for the parameter (boldsymbol{mu}_{c})

Assuming \(\boldsymbol{\Sigma}_{c}=\mathbf{I}\) for all classes, compute the posterior density \(p\left(\boldsymbol{\mu}_{c} \mid \mathbf{X}^{c}\right)\) for the parameter \(\boldsymbol{\mu}_{c}\) of a Bayesian classifier where the set of training objects in class \(c\) is given by \(\mathbf{x}_{1}, \ldots, \mathbf{x}_{N_{c}}\). Assume a Gaussian prior on \(p\left(\boldsymbol{\mu}_{c}\right)\).