For a binary classification problem, you are given the input feature vectors $\{$X$1,...,$XN $\}$ and the output class labels $\{$y$1,...,$yN $\}$ of N independent training instances, where yi in $\{0,1\}.$ Given each class, use the Gaussian likelihood for data instances. a$)$ Write the posterior class probability using the Bayes theorem. In the posterior expression, label each term involved. b$)$ Draw the graphical model for the generative model by denoting the class prior probability with $\backslash$pi $.$ Show also the likelihood parameters in the graph. $($Can use Python or draw by hand$)$ c$)$ Explain how to train the generative model and how to classify a test instance.