In the following profit payoff table for a decision problem with two states of nature and three decision alternatives, the prior probabilities for s1 and s2 are P(s1) = .8 and P(s2) = .2.

a. What is the optimal decision?
b. Find the EVPI.
c. Suppose that sample information I is obtained, with P(I | s1) = .20 and P(I | s2) = .75.
Find the posterior probabilities P(s1 | I) and P(s2 | I). Recommend a decision alternative based on these probabilities

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State of Nature Decision Alternative di d. 15 10 10 12 20 d.