Suppose we have a data set {(x1,y1),..., (XN, YN)}. xi's and labels yi's are both binary: i.e., xi, Yi {0, 1} for all i. We know the generating process of this dataset: for each (xi, Yi), first label y are generated from the Bernoulli distribution: Yi ~ Bernoulli(1/2). In other words, Pr(yi = 1) = Pr(yi = 0) = 1/2. Then, if y = 1, then xi ~ Bernoulli(p), if y = 0, then xi Bernoulli(g). In other words, Pr(xi = 1 | Yi = 1) = p, Pr(xi = 1 | Yi = 0) = q. Suppose p > q, we would like to find the Bayes optimal classifier f* : Y, which predicts label yi based on xi. (i) (Points: 10) What is the Bayes optimal classifier f*(x)? (ii) (Points: 10) Prove that the classifier has minimal risk among all deterministic classifiers. ~