4. 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 rough 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. The final exam result depends on how much they study and on the difficulty of the course. Their final grade (A, B, C or F) 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 utility depends on their subjective total effort and their final grade.

Suppose their subjective total effort (a lot or a little) depends on their 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 is lazy and just wants to pass

(not get an F). The total effort here measures whether they (thought they) worked a lot or a little overall. Explain the best outcome and the worst outcome. Fill in copy of the table of Figure 9.24; use 100 for the best outcome and 0 for the worst outcome.

(f) Given your utility function for the previous part, give values for the missing terms for one example that reflects the utility function you gave above :
Comparing outcome ____________________ and lottery [p:_____________________, 1 − p:____________________]
when p = ____________ the outcome is preferred to the lottery when p = ____________ the lottery is preferred to the outcome.
(g) Give an appropriate utility function for a student who does not mind working hard and really wants to get an A, and would be very disappointed with a B or lower. Explain the best outcome and the worst outcome. Fill in copy of the table of Figure 9.24; use 100 for the best outcome and 0 for the worst outcome.