Suppose a student’s final grade for a subject is determined by the difficulty of the subject and the student’s innate intelligence (ignoring the impact of the student’s effort). Build an OOBN to model the situation where each student takes multiple subjects, and each subject has multiple students, but not all students take each subject.

 Assuming the same prior for each student, but different priors for the difficulty of each subject, show how adding the students’ grades changes the posteriors for each student’s intelligence.

 Assuming you start with no information about each subject’s difficulty, but a good estimate of each student’s intelligence from their university entrance score, show how adding the students’ grades changes the posteriors for each subject’s difficulty.