Exercise 9.1 Students have to make decisions about how much to study for each course. The aim of this question is to investigate how to use decision networks to help them make such decisions.

Suppose students first have to decide how much to study for the midterm.

They can study a lot, study a little, or not study at all. Whether they pass the midterm depends on how much they study and on the difficulty of the course.

As a first-order approximation, they pass if they study hard or if the course is easy and they study a bit. After receiving their midterm grade, they have to decide how much to study for the final exam. Again, the final exam result depends on how much they study and on the difficulty of the course. Their final grade depends on which exams they pass; generally they get an A if they pass both exams, a B if they only pass the final, a C if they only pass the midterm, or an F if they fail both. Of course, there is a great deal of noise in these general estimates.

Suppose that their final utility depends on their total effort and their final grade. Suppose the total effort is obtained by adding the effort in studying for the midterm and the final.

(a) Draw a decision network for a student decision based on the preceding story.

(b) What is the domain of each variable?

(c) Give appropriate conditional probability tables.

(d) What is the best outcome (give this a utility of 100) and what is the worst outcome (give this a utility of 0)?

(e) Give an appropriate utility function for a student who just wants to pass (not get an F). What is an optimal policy for this student?

(f) Give an appropriate utility function for a student who wants to do really well. What is an optimal policy for this student?