Assume that a patient is believed to have one of two diseases, denoted by D1 and D2 with P(D1)=0.40 and P(D2)=0.60 and that medical research has determined the probability associated with each symptom that may accompany the diseases. Suppose that given diseases D1 and D2, the probabilities that the patient will have symptom S1, S2 or S3 are as sollows:
S1 S2 S3
D1 0.15 0.10 0.15
D2 0.80 0.15 0.03
After a certain symtom is found to be present, the medical diagnosis will be aided by finding the revised probability of each disease. Compute the posterior probability of each disease given the following medical findings:
a. The patient has symptom S1
b. The patient has symptom S2
c. The patient has symptom S3
d. For the patient with symptom S1 in part a), supposed we also find symptom S2. What are the revised probabilities of D1 and D2?
e. If the probabilities for D1 and D2 are 0.25 and 0.75, respectively, compute the revised probability in part d).
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Bayesian analysis problems and solutions
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1. A product's failure time follows the Weibull distribution with the CDF:
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