Question: 16. Posterior Probabilities Calculation. Suppose that you are given a decision situation with three possible states of nature: s1, s2, and s3. The prior probabilities

16. Posterior Probabilities Calculation. Suppose that you are given a decision situation with three possible states of nature: s1, s2, and s3. The prior probabilities are P(s1) 5 0.2, P(s2 ) 5 0.5, and P(s3 ) 5 0.3. With sample information I, P(I | s1) 5 0.1, P(I | s2 ) 5 0.05, and P(I | s3 ) 5 0.2. Compute the revised (or posterior) probabilities:

P(s1 | I ), P(s2 | I ), and P(s3 | I ).

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