whether zan 5%. APPENDIX 2.1: DERIVATION OF BAYES' THEOREM Case Study WTVX WTVX, Channel 6, is located in Eugene, Oregon, home of the University of Oregon's football team. The station was owned would be phoned in, and they were answered on the spot by Joe. ether and operated by George Wilcox, a former Duck (University Once a 10-year-old boy asked what caused fog, and Joe did an excellent job of describing some of the various causes. of Oregon football player). Although there were other televi- sion stations in Eugene, WTVX was the only station that had Occasionally, Joe would make a mistake. For example, a high school senior asked Joe what the chances were of getting 15 a weatherperson who was a member of the American Meteo- days of rain in the next month (30 days). Joe made a quick calcu- rological Society (AMS). Every night, Joe Hummel would be lation: (70%) X (15 days/ 30 days) = (70%) (1/2) = 35%. introduced as the only weatherperson in Eugene who was a Joe quickly found out what it was like being wrong in a univer- member of the AMS. This was George's idea, and he believed sity town. He had over 50 phone calls from scientists, mathema- that this gave his station the mark of quality and helped with ticians, and other university professors, telling him that he had market share. made a big mistake in computing the chances of getting 15 days In addition to being a member of AMS, Joe was also the of rain during the next 30 days. Although Joe didn't understand most popular person on any of the local news programs. Joe all of the formulas the professors mentioned, he was determined was always trying to find innovative ways to make the weather to find the correct answer and make a correction during a future interesting, and this was especially difficult during the winter broadcast . months when the weather seemed to remain the same over long periods of time. Joe's forecast for next month, for example, was Discussion Questions that there would be a 70% chance of rain every day, and that what happens on one day (rain or shine) was not in any way 1. What are the chances of getting 15 days of rain during the dependent on what happened the day before. next 30 days? # One of Joe's most popular features of the weather report 2. What do you think about Joe's assumptions concerning was to invite questions during the actual broadcast. Questions the weather for the next 30 days? Bibliography G. Reitsch, and D. W. Wichern. Business Forecasting