The operations manager for a community bus company wants to decide whether he should purchase a small, medium, or large new bus for his company. He estimates that the annual profits (in $000) will vary depending upon whether passenger demand is low, medium, or high as follows:
Bus Low Medium High
Small 50 60 70
Medium 40 80 90
Large 20 50 120
Prior Probabilty low .3 medium .3 high .4
If he uses the maximax criterion, which size bus will he purchase?
If he uses the maximin criteria, which size bus would he purchase?
If he uses Bayes' decision rule, which size bus would he purchase?
What is the expected annual profit for the bus that he will decide to purchase using Bayes' decision rule?