Problem 6 Evaluation (20 pts.) Suppose that you are working for a phone company that wants to predict churn. Churn is when customers cancel their subscriptions. Let x designate a customer, let actual be a binary random variable meaning that the customer actually churns, and let flag be a binary random variable meaning that a classifier predicts that the customer will churn. Note that Plactual 1) is the churn base rate, that is the fraction of customers that really do churn. Similarly, P[flag 1) is the fraction of customers that are predicted to churn, we know that the churn base rate is 5% Define a : Plactual = 11 flag : 1) and b-p(actual :01 flag :0). You have hired Dr. Lin as a data mining consultant. He claims that he can train a classifier that will achieve a = 0.8 and b = 0.9. (a) write down a confusion matrix and show how to define P(actual : 1) and P(flag-1) in terms of the entries in the confusion matrix. (8pts) (b) Show how to define a and b in terms of the entries in the confusion matrix. (8 pts) (c) Prove Dr. Lin wrong, because no such classifier exists. (4pts)