[Solved] CptS540 Artificial Intelligence Homework 8

1. Construct a Bayesian network (showing all nodes, links, and conditional probability tables) that is consistent with the below full joint probability distribution below over four Boolean random variables (Party, Sleep, Study, Pass) and consistent with the following three conditions. Round each probability in the conditional probability tables to the nearest tenth.
   • Sleep is conditionally independent of Study given Party.
   • Study is conditionally independent of Sleep given Party.
   • Pass is conditionally independent of Party given Sleep and Study.

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2. Compute the probabilities below based on the following Bayesian network. Show your work.

1. P(EatRight=true, Exercise=true, Healthy=true, LiveLong=true, Prosper=true)?
2. P(Healthy=true | Exercise=false)?
3. P(LiveLong=true | EatRight=true, Exercise=true)?
4. P(EatRight=true | LiveLong=true, Prosper=true)?
5. P(Prosper | EatRight=false, Exercise=false)?

3. What would be the most likely sample from applying direct sampling to the Bayesian network in Problem 2? What is this samples probability?

4. CptS 540 Students Only. Consider the Bayesian network below, where each of the five random variables have a domain of 4 values. What is the minimum number of probabilities needed to completely describe the full joint probability distribution for this scenario? Justify your answer.

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