Problem 3: (10 points) Decision Trees Consider the table of measured data given at right. (Note that some data points are repeated.) We will use a decision tree to predict the outcome y using the three features, xi, , :3. In the case of ties, we prefer to use the feature with the smaller index (xi over r2, etc.) and prefer to predict class 1 over class 0. You may find the following values useful (although you may also leave logs unexpanded) log2(1) 0 log2(2) log2(3) 1.59 log2(4) 2 log2(5) -2.32 log2(6) 2.59 log2(7) 2.81 log2(8) 3 100 1 1001 101 0 (a) What is the entropy of y'? (b) Which variable would you split first? Justify your answer (c) What is the information gain of the variable you selected in part (b)