Module 3 (Version B) Solution

Total points 20/20







This module is worth 20 points. Your last submission will be used for the Fnal score. You may attempt this module 5 times without penalty. After 5 attempts, each additional attempt will result in a penalty of 5% (e.g., On your 7th attempt, you obtain a score of 18 points. Then, your Fnal score for this module will be 18 - (2*1) = 16 points.)




If you encounter any problems with the assignment, please email zheweisun@cs.toronto.edu with [CSC384 A4] in the subject. Be sure to include the module number and version.




























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CSC384 S19 A4 Module 3 (Version B) 2019-07-30, 1*31 AM



















M3P1 – D-Separation







Answer the following True/False questions based on the following graph:




Section score 4/4


















































































A and B are independent, given no evidence.




True







False










A and B are conditionally independent, given C.




True







False




























































































































1/1


































1/1
























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CSC384 S19 A4 Module 3 (Version B) 2019-07-30, 1*31 AM













D and E are conditionally independent, given C.




True







False










D and E are conditionally independent, given A and B.




True







False











































M3P2 – Variable Elimination I







Answer the questions based on the following Bayes net:




Section score 6/6










1/1


































1/1











































































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CSC384 S19 A4 Module 3 (Version B) 2019-07-30, 1*31 AM








































































































































Select all that are true:
2/2



Pr(X2 = T | X3 = F) = Pr(X2 = T, X3 = F) / Pr(X3 = F)







Pr(X2 = T | X3 = F) = Pr(X2 = T, X3 = F) / [ Pr(X2 = T, X3 = F) + Pr(X2 = F, X3 = F)]




Pr(X2 = T | X3 = F) = Pr(X2 = T, X3 = F) / [ Pr(X2 = T, X3 = T) + Pr(X2 = T, X3 = F)]




Pr(X2 = T | X3 = F) = Pr(X2 = T, X3 = F) / Pr(X2 = T)
























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CSC384 S19 A4 Module 3 (Version B) 2019-07-30, 1*31 AM













Calculate the following:
1/1










































Solve P(X2 = T | X3 = F).
3/3



*Hint: Using variable elimination with elimination ordering X4, X1, X2, X3 will greatly simplify your calculations! The two previous questions should also guide your calculations. Your answer should be between 0 and 1, rounded to 3 digits after the decimal (e.g. 0.120).























































M3P3 – Variable Elimination II







Section score 10/10

























































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CSC384 S19 A4 Module 3 (Version B) 2019-07-30, 1*31 AM



























































































Given the table of probabilities pictured, what is P(C = -c | D = - 5/5 d)?




Your answer should be between 0 and 1, rounded to 3 digits after the decimal (e.g. 0.120).






















Given the table of probabilities pictured, what is
5/5
P(E=e|A=a,D=d)?





Your answer should be between 0 and 1, rounded to 3 digits after the decimal (e.g. 0.120).








































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