(a) Given the following decision tree, show how the new examples in the table would be classified by filling in the last column in the table. If an example cannot be classified, enter UNKNOWN in the last column. (2 marks) (b) We would like to predict the sex of a person based on two binary attributes: leg-cover (pants or skirts) and facial-hair (some or none). We have a data set of 2,000 individuals, half male and half female. 75% of the males have no facial hair. Skirts are wom by 50% of the females. All females are barefaced and no male wears a skirt. For your information, log(1/8)=3.00,log2(1/4)=2.00,log2(1/3)=1.58,log2(3/8)= 1.42,log2(3/7)=1.22,log2(1/2)=1.00,log2(4/7)=0.81,log2(5/8)=0.68, log2(2/3)=0.58,log2(3/4)=0.42,log2(7/8)=0.19 (i) What is the initial entropy in the system? ( 2 marks) (ii) Compute the information gain of initially choosing the attribute leg-coner and for initially choosing facial-hair. (4 marks) (iii) Based on yours answers, which attribute should be used as the root of a decision tree? (2 marks)