CptS540 Artificial Intelligence – Homework 8 Solved

Description

 

 

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.

 

Party	Sleep	Study	Pass	Probability
true	true	true	true	0.0216
true	true	true	false	0.0024
true	true	false	true	0.0224
true	true	false	false	0.0336
true	false	true	true	0.0216
true	false	true	false	0.0144
true	false	false	true	0.0084
true	false	false	false	0.0756
false	true	true	true	0.3024
false	true	true	false	0.0336
false	true	false	true	0.0896
false	true	false	false	0.1344
false	false	true	true	0.0864
false	false	true	false	0.0576
false	false	false	true	0.0096
false	false	false	false	0.0864

 

 

 

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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 sample’s 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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