### Artificial IntelligenceAIMA Exercises

In the recursive construction of decision trees, it sometimes happens that a mixed set of positive and negative examples remains at a leaf node, even after all the attributes have been used. Suppose that we have $p$ positive examples and $n$ negative examples.
1. Show that the solution used by DECISION-TREE-LEARNING, which picks the majority classification, minimizes the absolute error over the set of examples at the leaf.
2. Show that the class probability $p/(p+n)$ minimizes the sum of squared errors.

In the recursive construction of decision trees, it sometimes happens that a mixed set of positive and negative examples remains at a leaf node, even after all the attributes have been used. Suppose that we have $p$ positive examples and $n$ negative examples.
1. Show that the solution used by DECISION-TREE-LEARNING, which picks the majority classification, minimizes the absolute error over the set of examples at the leaf.
2. Show that the class probability $p/(p+n)$ minimizes the sum of squared errors.

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