would also like the justification for the answers where it asks.

this question is on bayesian networks. the questions are regarding the network shown above in the diagram

Problem 1. Consider the following Bayesian network with 6 nodes. A B D E F 2. Suppose each random variable takes three states, i.e., A can take values in {20,21,22}, B can take values in {bo, b1,b2} and so on. What is the minimum number of parameters to exactly express the above model, i.e., to express the joint distributions p(A, B, C, D, E, F) (2.5 marks)? Please also justify your answer (2.5 marks). (In total 5 marks) 3. Check whether the following statements are true. If you think the statements are true, then type T, otherwise type F. Please just type five characters for the five questions in order. For example, if you think the first four are true and the last is false, then simply type TTTTE. We also need you to justify your answer in the last bullet. A and B are independent (0.5 mark) - A and B are conditionally independent given D (0.5 mark) - A and E are conditionally independent given D (0.5 mark) - E and F are independent (0.5 mark) - E and F are conditionally independent given D (0.5 mark). Use the expression of joint distribution to justify your answer, i.e., either prove the independency or show it does not hold (2.5 marks). Hint: there is no need to consider all random variables in the Bayesian network