You work for an insurance company and are using a mutual information based decision tree method to classify customers into three classes: low risk, medium risk and high risk. The idea is to accept all low risk and to reject all high risk customers and medium risk customers will be given a telephone interview to decide.

(a) Briefly explain how mutual information can be used in decision trees for classification purposes in the above example.

(b) One of the attributes you use is annual income. Your decision tree has rules defined for income values between 0 and 10,000,000. Unfortunately, one customer has entered -1 as a value for annual income and your decision tree execution stops. What did you forget to implement and how would you fix it in this example.

(c) You observe the running of your decision tree algorithm in detail and notice that two customers who are almost identical, just differing in one attribute, end up in different classes. On the other hand, you notice two customers with many different attribute values ending up in the same class. Please explain whether this means your decision tree is working well or not. [2 marks]