I need help with the attached problem.

1. Bayes Network. Incidences of diseases A and B (D ,4, DB] depend on the exposure {E}. Disease A is additionally inuenced by risk factors (R). Both diseases lead to symptoms (S). Results of the test for disease A (TA) are a'ected also by disease B. Positive test will be denoted as TA = 1, negative as TA = 0. The Bayes Network is shown in Figure 1. Needed conditional probabilities are shown in Table 1. 9 9 Figure 1: The DAG of the Bayesian networks Table 1: The known (or elicited} conditional probabilities E 0 1 R 0 1 0.8 0.2 0.? 0.3 Ba 0 1 E\" 0.8 02 E 0.3 07 D3303 0.95 0.05 D3393 0.92 0.08 DZDB 0.0 0.4 D333 0.8 0.2 DAD'JB 0.4 0.0 BADGE 0.15 0.85 DAD}; 0.1 0.9 DADS 0.03 0.97 (a) What is the probability of disease A (By, = 1}, if disease B is not present (D3 = 0}, but symptoms are present (8 = 1). (b) What is the probability of exposure (E = 1), if symptoms are present {3 = 1) and test is positive (TA = 1). Hint: You can solve this problem by any of the 3 ways: (i) use of WinBUGS or Open- 2 BUGS, (ii) direct simulation using Octave ,1 MATLAB, R, or Python, and {iii} exact calcula- tion