is considering whether to hold an extensive campaign next year to raise funds for a new athletic field. The response to the campaign depends heavily on the success of the football team this fall. In the past, the football team has had winning seasons 60 percent of the time. If the football team has a winning season (W) this fall, then many of the alumni will contribute and the campaign will raise $3 million. If the team has a losing season (L), few will contribute and the campaign will lose $2 million. If no campaign is undertaken, no costs are incurred. On September 1, just before the football season begins, the Athletic Department needs to make its decision about whether to hold the campaign next year. Questions: 1/ Formulate the payoff table by identifying the decision alternatives, the states of nature. 2/ According to four criteria, which alternative will be chosen? 3/ What is the expected value of perfect information? 4/ A famous football guru, TBC, has offered his services to help evaluate whether the team will have a winning season. For $100,000, he will carefully evaluate the team throughout spring practice and then throughout preseason workouts. TBC then will provide his prediction on September 1 regarding what kind of season, W or L, the team will have. In similar situations in the past when evaluating teams that have winning seasons 50 percent of the time, his predictions have been correct 75 percent of the time. Considering that this team has more of a winning tradition if William predicts a winning season, what is the posterior probability that the team actually will have a winning season? What is the posterior probability of a losing season? 5/ Draw the decision tree for this entire problem. Analyze this decision tree to determine the optimal policy regarding whether to hire TBC and whether to undertake the campaign. 6/ Find the expected value of sample information. If the fee for hiring TBC is open to negotiation, how large can TBC’s fee be and still be worthwhile?
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