# dolution

You are given the following payoff table (in units of dollars): You have the option of paying \$100 to have research done to better predict which state of nature will occur. When the true state of nature is S1, the research will accurately predict S1 60 percent of the time (but will inaccurately predict S2 40 percent of the time). When the true state of nature is S2, the research will accurately predict S2 80 percent of the time (but will inaccurately predict S1 20 percent of the time).

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(a) Given that the research is not done, use BayesĂ˘â‚¬â„˘ decision rule to determine which decision alternative should be chosen.

(b) Find EVPI. Does this answer indicate that it might be worthwhile to do the research?

(c) Given that the research is done, find the joint probability of each of the following pairs of outcomes: (i) the state of nature is S1 and the research predicts S1, (ii) the state of nature is S1 and the research predicts S2, (iii) the state of nature is S2 and the research predicts S1, and (iv) the state of nature is S2 and the research predicts S2.

(d) Find the unconditional probability that the research predicts S1. Also find the unconditional probability that the research predicts S2.

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