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solution

The marketing department of a riding mower manufacturer wants to understand who are more likely to buy their riding mowers. A group of data analysts is building a classification tree to classify its customers into two classes: nonowners (class 0) and owners (class 1) of riding mowers. Each customer is described by two attributes: income and lot size. The data analysts have agreed to split a set of training records (denoted by A) using customer’s lot size. Two subsets of records (denoted by A1 and A2 respectively) are produced after splitting A. The number of nonowners and owners in A, A1, and A2 are given below. Keep at least three digits after the decimal point.

A A1 A2
Number of Nonowners 56 49 7
Number of Owners 104 44 60

Please answer the following questions:

A A1 A2
The proportion of Nonowners (p0)
The proportion of Owners (p1)
Entropy

What is the combined entropy of A1 and A2?

How much is the reduction in entropy if training records are split by customer’s lot

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