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 currently under consideration. The 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 and the current one. The engine for the current order will be produced in the same plant as the previous model, although the Air 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 required for the older version, but the supplier has not revealed the production location.
(a) How much money is it worthwhile to pay for perfect information on which plant will produce these engines?
(b) Assume that the cost of the data on the old airplane model is free and that 30 spares were required. You are given that the probability of 30 spares, given a Poisson distribution with mean θ, is 0.013 for θ = 21 and 0.036 for θ = 24. Find the optimal action under Bayes’ decision rule.