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).

(a) Given that the research is not done, use Bayes’ 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.