2. In a classication problem with two classes and two features, the joint distribution of the features in each class is: 1 2 #031,322) = eXP - 2w (1k/4) 2(1-k/4) ' k=1'2 where z = (x1 R02 @(xl k)(x2 k2) + (2:2 14:2)2 (a) Assuming that the prior probability of class one is twice the prior probability of class two, in what class is the point (X1, X2) = (1, 5) is classied? (b) The marginal distributions of features in each class can be calculated from the joint distributions, and are: l. (IE1 k)2 m = ex M 1) m p 2 1 (m2 m2 :1: = ex The Naive Bayes assumption clearly does not hold in this problem. However, clas sify (X1, X 2) = (1, 5) pretending the Naive Bayes assumption holds and compare the results with part 2a