Problem 3 Robert is trying to decide whether to study hard for the Bayesian Artificial Intelligence exam. He would be happy with a good mark (e.g., a High Distinction) for the subject, but he knows that his mark will depend not only on how hard he studies but also on how hard the exam is and how well he did in the Introduction to Artificial Intelligence subject (which indicates how well prepared he is for the subject).

Build a decision network to model this problem, using the following steps.

???? Decide what chance nodes are required and what values they should take.

???? This problem should only require a single decision node; what will it represent?

???? Decide what the casual relationships are between the chance nodes and add directed arcs to reÐect them.

???? Decide what chance nodes Robertís decision may effect and add arcs to reÐect that.

???? What is Robertís utility function? What chance nodes (if any) will it depend on? Does it depend on the decision node? Will a single utility node be sufÝcient?

Update the decision network to reÐect these modeling decisions.

???? Quantify the relationships in the network through adding numbers for the CPTs (of chance nodes) and the utility table for the utility node. Does the number of parameters required seem particularly large? If so, consider how you might reduce the number of parameters.

???? Once you have built your model, show the beliefs for the chance nodes and the expected utilities for the decisions before any evidence is added.
???? Add evidence and see how the beliefs and the decision change, if at all.
???? If you had an information link between the evidence node and the decision node, view the decision table.
???? Perform your own decision tree evaluation for this problem and conÝrm the numbers you have obtained from the software.