Homework 1
ECE 285
1. (25 points) For the following Bayesian network, judge whether the following statements are
true or false. And give a brief explanation for each of your answer.
(I: Intelligent; H: Hardworking; T: good Test taker; U: Understands material; E: high Exam score)
• T and U are independent.
• T and U are conditionally independent given I, E, and H.
• T and U are conditionally independent given I and H.
• E and H are conditionally independent given U.
• E and H are conditionally independent given U, I, and T.
• I and H are conditionally independent given E.
• I and H are conditionally independent given T.
• T and H are independent.
• T and H are conditionally independent given E.
• T and H are conditionally independent given E and U.
2. (15 points) For the above Bayesian network, construct local conditional probability tables.
Assume all variables are binary (1 for true and 0 for false). For example, p(E=1|T=1, U=1) = 0.8.
And give a brief explanation for your specified probabilities. For example, if a student is a good
test taker and understands the material well, the student is very likely to have a high exam
score.
3. (10 points) For the above Bayesian network, write down the joint distribution of all variables.
4. (15 points) Calculate P(E=1|Hardworking=1).
5. (35 points) Consider a task: based on the infected cases in the past week, predict the number
of infected COVID-19 cases for all cities in San Diego County for tomorrow. Design a Markov
random field model to perform this task. In the model, capture the correlation between cities:
nearby cities have similar number of infected cases.
