Suppose you have a 2~class classication problem, where each class is Gaussian. Let 6 = {(1, p1, 21,,u2, 22} denote the set of model parameters. Suppose the class probability p(y|9) is modelled via the Bernoulli distribution, Le. p(y|9) = (19(1 (1)1'9, and the probability of the data p(:r:|y, 3) is modelled as p(:1:|y, 9) = N(I[y, 2y). Recover the parameters of the model from maximum likelihood approach. Assume the data are i.i.d. and N is the number of data samples. Show all derivations. Next, suppose you want to make a classication decision by assigning proper label 3; to a given data point 3:. You decide the label based on Bayes optimal decision y = arg maxi-pm,\" p(g}|:r). Prove that the decision boundary is linear when covariances El and 22 are equal and otherwise the boundary is quadratic. Illustrate on 2d example the decision boundary for the case when covariances are not equal clearly indicating which class is more concentrated around its mean