7. [20 points] Consider a 2-class problem in a 1-dimensional space. Density function for class 0 is given by a Gaussian: P(x|0) = G(x|Mo, ?) . Density function of class 1 is given by a Gaussian P(x|1) = G(x|M1, of). . Also, the priors of the two classes are unknown and given It = P(0) and (1 - IT) = P(1). Given a weighted dataset {(Wn Xn n)In where wn is the weight and yn E {0,1} is the class label for the nth data point: (a) [5 points] Let's formulate this as a maximum likelihood optimization problem. N J (n, Mo, M1, 08, 07) = [P (xn, 0) 1 - YnP(Xn, 1) Yn]Wn n=1 Refine and simplify this objective function. (b) [4 points] Solve for It (c) [5 points] Solve for the two means: Mo and M1 (d) [6 points] Solve for the two variances: of and of Note that all the answers should be in terms of the data {(Wn, In, Vn)) and N