The next two questions refer to the following belief network with random variables F0,F1,…,F4 which only take the values 0 and 1. Which of the following statements are true about this belief network (1), (3) and (4) only : (1) F0 and F3 are independent given F1,F2 ; (2) F0 and F2 are independent; (3) P(F0∣F1,F2)=P(F0∣F1,F2,F3,F4) ; (4) F0 and F4 are independent. In general, to define the joint probability distribution P(F0,…,F4) one requires up to 25−1 entries in the table of probabilities. For the belief network above, one can compute the joint probability distribution P(F0,…,F4) using the following number of conditional probabilities

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The next two questions refer to the following belief network with random variables
F0,F1,…,F4 which only take the values 0 and 1.

 

Which of the following statements are true about this belief network (1), (3) and (4) only :

(1) F0 and F3 are independent given F1,F2 ;
(2) F0 and F2 are independent;
(3) P(F0∣F1,F2)=P(F0∣F1,F2,F3,F4) ;
(4) F0 and F4 are independent.


In general, to define the joint  probability distribution P(F0,…,F4) one requires up to 25−1 entries in the table of probabilities. For the belief network above, one can compute the joint probability distribution P(F0,…,F4) using the following number of conditional probabilities

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