The figure below shows a Bayesian Net characterizing the causal relationship between 5 random variables X1,...

Transcribed Image Text:

The figure below shows a Bayesian Net characterizing the causal relationship between 5 random variables X1, X2, X3, X4 and X5 where X1, X2, X4 {0, 1} while X3, X5 {0, 1, 2}. X2 X3 X4 X5 Answer the following questions: A. Write down the factorized expression of the joint probability of P(X1, X2, X3, X4, X5) as indicated by the Bayesian Net. [5pts] B. If X4 is observed while the rest of the variables are unobserved, are X1 and X5 (conditionally) independent? Explain. [5pts] C. Given the prior and conditional probability tables below for the above Bayesian Net, compute P(X1 | X3 = 1, X2) for all possible value assignments for (X1, X2). [10pts] 1 X2 X3 p(x3|x1,x2) 1 p(x1) X2 p(x2) 0 0 0 0.3 0 0.6 0 0.7 0 0 1 0.4 0 1 0 0.9 0 1 1 0.08 X3 X4 P(x4|x3) 1 0 0 0.05 0 0 0.1 1 0 1 0.25 1 0 0.4 1 1 0 0.5 2 0 0.99 1 1 1 0.3 The figure below shows a Bayesian Net characterizing the causal relationship between 5 random variables X1, X2, X3, X4 and X5 where X1, X2, X4 {0, 1} while X3, X5 {0, 1, 2}. X2 X3 X4 X5 Answer the following questions: A. Write down the factorized expression of the joint probability of P(X1, X2, X3, X4, X5) as indicated by the Bayesian Net. [5pts] B. If X4 is observed while the rest of the variables are unobserved, are X1 and X5 (conditionally) independent? Explain. [5pts] C. Given the prior and conditional probability tables below for the above Bayesian Net, compute P(X1 | X3 = 1, X2) for all possible value assignments for (X1, X2). [10pts] 1 X2 X3 p(x3|x1,x2) 1 p(x1) X2 p(x2) 0 0 0 0.3 0 0.6 0 0.7 0 0 1 0.4 0 1 0 0.9 0 1 1 0.08 X3 X4 P(x4|x3) 1 0 0 0.05 0 0 0.1 1 0 1 0.25 1 0 0.4 1 1 0 0.5 2 0 0.99 1 1 1 0.3