Using the posterior computed in the previous exercise, compute the expected likelihood:

\[p\left(\mathbf{x}_{\text {new }} \mid T_{\text {new }}=c, \mathbf{X}, \mathbf{t}\right)=\mathbf{E}_{p\left(\boldsymbol{\mu}_{c}, \boldsymbol{\Sigma}_{c} \mid \mathbf{X}^{c}\right)}\left\{p\left(\mathbf{x}_{\text {new }} \mid \boldsymbol{\mu}_{c}, \boldsymbol{\Sigma}_{c}\right)\right\}\]