Consider the data set shown in Table 5.2.
(a) Estimate the conditional probabilities for P(A = 1|+), P(B = 1|+),
P(C = 1|+), P(A = 1|−), P(B = 1|−), and P(C = 1|−) 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 = 1) using the naive Bayes approach.
(c) Compare P(A = 1), P(B = 1), and P(A = 1,B = 1). State there lationships between A and B.
(d) Repeat the analysis in part (c) using P(A = 1), P(B = 0), and P(A =
1,B = 0).
(e) Compare P(A = 1,B = 1|Class = +) against P(A = 1|Class = +) and P(B = 1|Class = +). Are the variables conditionally independent given the class?