Question 1 5 points/ Decision Tree Classification In the recursive construction of decision trees, we may sometimes produce a leaf node based on a mixed set of positive and negative examples _ e.g., due to pruning, or perhaps after all the attributes have been used. Here, suppose that P positive and N negative examples reach some leaf node a 21: One approach is to return the majority classification -i.e., "true" if P > N; else "false". Show that this approach minimizes the 0/1 over the set of examples that reach this leaf node. b [3]: Alternatively, suppose the decision tree, on reaching this leaf, returns the probability [0, 1 j, corresponding to the (predicted) probability that an instance reaching here belongs to the positive class. This means the "squared error" for each positive instance is (1-a)2 as the decision tree should have returned 1 here; and the squared error for each negative instance is (0-a)2. Find the value of (as a function of P, N, and any other relevant aspect, such as number of attributes, etc.) that minimizes the sum of these squared errors