How do you do question 16.3-9 part a-f

PROBLEMS data have been obtained that provide 1638 Reconsider Prob 16.2-8. Suppose now that the Air Force knows that a similar type of engine was produced for an earlier version of the type of airplane curremtly under consideration. The similaraod of obtaining s of land favorable seismic soundings are ob- Specifcall order size for this earlier version was the same as for the current type. Furthermore, the probability distribution of the number of spare engines required, given the plant where production takes place, is believed to be the same for this earlier airplane model changes to 40 the new posterior probabilities. e for posterior probabilities to check mal policy? ving payoff table (in units of doflars): The engine for the current order will be pro- in the same plant as the previous model, although the Air and the current one. Force does not know which of the two plants this is. The Air Force does have access to the data on the number of spares actually re quired for the older version, but the supplier has not revealed the the older State of Nature production locatior. (a) How much money is it worthwhile to pay for perfect infor- (b) Assume that the cost of the data on the old airplane model is mation on which plant will produce these engines? 400 free and that 30 spares were required. You are given that the probability of 30 spares, given a Poisson distribution with mean , is 0.013 for e-21 and 0.036 for 24. Find the optimal action under Bayes' decision rule. 100 0.6 100 to have research done to bet6Vincent Cuomo is the credit manager for will occur. When the true state of Mill. curately predict S, 60 percent of s100,000 credit to a potential new customicr biness of a company: edict S2 40 percent of the time). Vincent has three categories for the credtwot S, the research will accurately (but will inaccurately predict S category fits this He is currently faced with the question of whether to extend of a poor risk, average risk, and good risk, but he does not know which category fits this potential customer. Experience indicates that 20 percent of companies similar to this dress manufacturer are poor risks, 50 percent are average risks, and 30 percent are good risks. If credit is extended, the expected profit for poor risks is-$15,000 for average risks $10,000, and for good risks $20,000. If credit is not extended, the dress manufacturer will turn to another mill. Vincent is able to consult a credit-rating organization for a fee of $5,000 per company evaluated. For companies whose actual credit record with the mill turns out to fall into each of the three categories, the following table shows the percentages that were given each of the three possible credit evaluations by the credit- done, use Bayes' decision rule ternative should be chosen. ndicate that it might be worth- , find the joint probability of utcomes: (1) the state of nature i, (i) the state of nature is S, c the state of nature is S2 and rating organization. ty that the research predicts probability that the research Actual Credit Record use your answers in parts sterior probabilities of the Credit Evaluation Poor Average Good wo possible predictions of Poor 50% Average Good 4096 50 2096 40 40 rior probabilities to obtain use Bayes' decision rule to e should be chosen and the (a) Develop a decision analysis formulation of this problem by iden- tifying the decision altematives, the states of nature, and the pay- off table when the credit-rating organization is not used redicts S2 the expected payoff when (b) Assuming the credit-rating organization is not used, use Bayes decision rule to determine which decision alternative should ne the optimal policy re- be chosen. nd the choice of the de- (e) Find EVPI.Does this answer indicate that consideration should be given to using the credit-rating organization