Suppose you have a 2class classication problem, Where each class is Gaussian. Let 6' = {mphghpmg} denote the set of model parameters. Suppose the class probability p{y|) is modelled via the Bernoulli distribution, i.e. p[y|t3) = dy 0:]1'1, and the probability of the data p[:|y,5j is modelled as p(z|y, I9} = N{2|py, Ely]; Recover the parameters of the model from maximuru likelihood approach [5 points for o, 10 points for it's, and 15 points for E's]. Assurue 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 = argmax={g11}p(g}|2r). Prove that the decision lxuundary is linear when covariances El and E; are equal and otherwise the boundary is quadratic. [5 points for each case] Illustrate on 2d example the decision boundary for the case when covariances are not equal clearl],r indicating which class is more concentrated around its mean [5 points].

Suppose you have a 2-class classication problem, where each class is Gaussian. Let 0 = {01,311, 21,;12, 22} denote the set of model parameters. Suppose the class probability p(y|t9) is modelled via the Bernoulli distribution, i.e. p(y|9) = (15\"(1 001'\