Artificial Intelligence - Conditional Dependency in a Bayesian Networ

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.

3 Bayesian 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 Tntelligent Hardworkin good Test taker material Pl-ul-i,-n) = .5 P(+ti)-.8 Pl-th) = .5 high Exa P(te-t,-u)-3 score Figure 1: A Bayesian network representing what influences an exam score Problem 5 (40 points.) For the above Bayesian network, label the following statements about conditional independence as true or false For this question, you should consider only the structure of the Bayesian network, not the specific probabilities. Explain each of your answers. Specifically, when you claim conditional dependence, you must show an active path 1. T and U are independent 2. T and U are conditionally independent given I, E, and H 3. T and U are conditionally independent given I and H 4. E and H are conditionally independent given U 5. E and H are conditionally independent given U, I, and T. 6. I and H are conditionally independent given E 7. I and H are conditionally independent given T. 8. T and H are independent. 9. T and H are conditionally independent given E 10. T and H are conditionally independent given E and U. 3 Bayesian 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 Tntelligent Hardworkin good Test taker material Pl-ul-i,-n) = .5 P(+ti)-.8 Pl-th) = .5 high Exa P(te-t,-u)-3 score Figure 1: A Bayesian network representing what influences an exam score Problem 5 (40 points.) For the above Bayesian network, label the following statements about conditional independence as true or false For this question, you should consider only the structure of the Bayesian network, not the specific probabilities. Explain each of your answers. Specifically, when you claim conditional dependence, you must show an active path 1. T and U are independent 2. T and U are conditionally independent given I, E, and H 3. T and U are conditionally independent given I and H 4. E and H are conditionally independent given U 5. E and H are conditionally independent given U, I, and T. 6. I and H are conditionally independent given E 7. I and H are conditionally independent given T. 8. T and H are independent. 9. T and H are conditionally independent given E 10. T and H are conditionally independent given E and U