Reconsider Prob. 16.2-4. Warren Buffy decides that Bayes’ decision rule is his most reliable decision criterion. He believes that 0.1 is just about right as the prior probability of an improving economy, but is quite uncertain about how to split the remaining probabilities between a stable economy and a worsening economy. Therefore, he now wishes to do sensitivity analysis with respect to these latter two prior probabilities.
(a) Reapply Bayes’ decision rule when the prior probability of a stable economy is 0.3 and the prior probability of a worsening economy is 0.6.
(b) Reapply Bayes’ decision rule when the prior probability of a stable economy is 0.7 and the prior probability of a worsening economy is 0.2.
(c) Graph the expected profit for each of the three investment alternatives versus the prior probability of a stable economy (with the prior probability of an improving economy fixed at 0.1). Use this graph to identify the crossover points where the decision shifts from one investment to another.
(d) Use algebra to solve for the crossover points identified in part (c).
(e) Develop a graph that plots the expected profit (when using Bayes’ decision rule) versus the prior probability of a stable economy.