Artificial Intelligence - Variable Elimination in Bayesian Networks

The letters refer to the ones written in red in the nodes. So I refers to the node "Intelligent". Also, the lowercase letters also refer to the same nodes. P(+i)= .7 refers to the "Intelligent" node. u would be the node "Understands material" and e would be the node "high Exam score".

3 Bavesian networks We are going to take the perspective of an instructor who wants to determine whether a student has understood the material, based on the exam score. Figure 1 gives a Bayesian network for this. As you can see, whether the student scores high on the exam is influenced both by whether she is a good test taker, and whether she understood the material. Both of those, in turn, are influenced by whether she is intelligent; whether she understood the material is also influenced by whether she is a hard worker P(ti)-.7 Intelligent Hardworkin good Test taker nderstandsP(+uti,+h) - .9 material high Exam\+)-.7 score Figure 1: A Bayesian network representing what influences an exam score. Problem 6 (30 points). Using variable elimination (by hand!), compute the probability that a student who did well on the test actually understood the material, that is, compute P(+ue) 3 Bavesian networks We are going to take the perspective of an instructor who wants to determine whether a student has understood the material, based on the exam score. Figure 1 gives a Bayesian network for this. As you can see, whether the student scores high on the exam is influenced both by whether she is a good test taker, and whether she understood the material. Both of those, in turn, are influenced by whether she is intelligent; whether she understood the material is also influenced by whether she is a hard worker P(ti)-.7 Intelligent Hardworkin good Test taker nderstandsP(+uti,+h) - .9 material high Exam\+)-.7 score Figure 1: A Bayesian network representing what influences an exam score. Problem 6 (30 points). Using variable elimination (by hand!), compute the probability that a student who did well on the test actually understood the material, that is, compute P(+ue)