2. 2.Consider the data set shown in Table below: Class Instance AB C 0 0 1 1 0 1 0 10 00 1 11 0 0 10 10 (a) Estimate the conditional probabilities for using the same approach as in the previous problem. (b) Use the conditional probabilities in part (a) to predict the class label for a test sample (A -1, B-1, C) using the naive Bayes approach. (c) Compare P (A-1), P (B-1), and P (A-1, 8-1) State the relationships between A and B (d) Repeat the analysis in part (c) using P (Ac1), P (8-0), and PA-1, B-0) (e) Compare P (A=1, B-11 Class-+) against P(Acil Class-+) and P (8-11 Class = +). Are the variables conditionally independent given the class? 3. For each of the Boolean functions given below, state whether the problem is linearhy separable. (a) A AND B AND C (b) NOT A AND B (c) (A OR B) AND (A OR C) (d) (A XOR B) AND (A OR B)