Consider values shown in the table below: i=1 (cold) i=2 (allergy) i=3 (stomach pain) p(Hi) 0.6 0.3 0.1 p(E1 |Hi) 0.3 0.8 0.3 p(E2 |Hi) 0.6 0.9 0.0 Those values represent (hypothetically) three...

Consider values shown in the table below:
i=1 (cold) i=2 (allergy) i=3 (stomach pain) p(Hi)
0.6
0.3
0.1 p(E1 |Hi)
0.3
0.8
0.3 p(E2 |Hi)
0.6
0.9
0.0
Those values represent (hypothetically) three mutually exclusive and exhaustive hypotheses for the patient’s condition. For example, H1: the patient has a cold, H2: the patient has an allergy, and H3: the patient has stomach pain with their prior probabilities, p(Hi)’s and two conditionally independent pieces of evidence (E1, patient sneezes and E2, patient coughs) which support these hypotheses to differing degrees. Therefore;
a) Compute the posterior probabilities for the hypothesis if the patient sneezes. What is the conclusion that can be derived from this condition?
b) Based on the answer from the previous result, as the patient coughs are now observed, compute the posterior probabilities for this condition. Explain the results.