Question 1: Using variable elimination (by hand!), compute the probability that

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Question 1: 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(+u| + e). Question 2: 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. 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. understood the material, that is, compute P(+u| + e). Question 2: 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. 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. 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. 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.

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I do not understand the problem, but may you please rate me as the lifesaver. I really need the points. Thank you.

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