Construct a tree diagram to describe the events in terms of the sequence of information provided above (missed payment, balance, previous payment amount). Note that this sequence is actually going backwards in time, but we will reverse that later. Label each branch as to the event it represents as well as the probability of travelling down that branch. If you are using labels, then you must define them (e.g., M = Missed payment). You may try to create the tree in Word, but you may find it easier to draw the tree by hand, take a picture and paste the picture into your assignment.

1. Calculate the final probabilities at the end of each branch and summarize them in a table like the one below:

	Missed Payment	On Time	Total
Balance > $3,000 Last Payment < 20%
Balance >$3,000 Last Payment >20%
Balance <$3,000 Last Payment < 20%
Balance < $3,000 Last Payment > 20%
Total

You may prefer to explore the tree and summarize the outcome by assuming that you are looking at 100,000 payment cases and find the frequency of occurrence of each outcome, but these should then be translated into the appropriate probabilities for the above table.

2. What is the probability that a customer has a balance over $3,000?
3. What is the probability that the customers previous payment was for more than 20% of the balance owing?
4. Among those with a balance exceeding $3,000, what proportion made their last payment on time?
5. Among those with a balance exceeding $3,000 and whose previous payment was for less than 20% of the balance owing, what proportion made their last payment on time?
6. SCU has decided to classify customers who owe more than $3,000 and whose previous payment was for less than 20% of the balance owing as High Risk to Default and all others as in Good Standing. Assuming this decision rule is applied to 100,000 cases, construct a confusion matrix that summarizes the decision and truth outcome frequencies. You should be able to do this by multiplying 100,000 times the appropriate probabilities from question 2.

Decision\Truth	Missed Payment	On Time	Total
High Risk to Default
Good Standing
Total			100,000

7. What is the Accuracy Rate of this decision rule in terms of classifying those as High Risk who then Miss Payment or those as in Good Standing who make their payment On Time? Explain Accuracy Rate in this situation in terms that SCU can understand.
8. What is the Sensitivity Rate of this decision rule? Explain what you mean by Sensitivity Rate in this situation.
9. What is the Specificity Rate of this decision rule? Explain what you mean by Specificity Rate in this situation.
10. What is the False Omission Rate of this decision rule? Explain what you mean by False Omission Rate in this situation.
11. What is the False Detection Rate of this decision rule? Explain what you mean by False Detection Rate in this situation.
12. You may feel that this classifier has not performed very well, because so many Missed Payment cases were not correctly detected and so many of those classified as High Risk actually paid on time. But what if you had no classifier at all? The nave strategy would be to classify every transaction as On Time since 94% of cases are On Time. What would be the Sensitivity Rate of this decision rule? What would be the False Detection Rate?

13. What could CSU do to improve the performance of their classifier used in question 7? There are numerous ways you can answer this question.