# Ms405

Topics: Dow Jones Industrial Average, Decision theory, Approximation Pages: 2 (687 words) Published: January 13, 2011
Question 1. Carla would like to open a small dress shop. At the present time, she believes that the chances of a successful or unsuccessful dress shop are about the same (50%). If Carla opens a shop and it is successful, she expects to make a profit of \$100,000. If she opens a shop that proves to be unsuccessful she will lose \$50,000. On the other hand, If Carla chose not to open her own shop, she would have the option of investing in a dress shop being started by her best friend Amanda. The probabilities of Amanda's shop being successful are the same as Carla's. Carla would only stand to make \$40,000 if the shop was successful but if it was unsuccessful she would only lose \$30,000. Of course Carla can always do nothing. Draw a decision tree for this problem. What is Carla's best strategy? Draw the risk profiles and cumulative risk profiles for the problem. Is there any kind of dominance among the possible alternative decisions? Explain. After a second thought Carla realizes that the profit she can make is not strictly \$100,000 but it can be as low as \$90,000 and as high as \$110,000. Conduct a one-way sensitivity analysis and draw a tornado diagram. e. What is the maximum amount of money that Carla should pay for information? f. In today's local paper, there was an article that described a study that can be done to indicate the potential of a retail store, which Carla believed could be applied to her idea, but not Amanda's. She found out that the probability of a favourable study given a successful shop P(favourable | SS) was 0.9. Furthermore the probability of an unfavourable study given an unsuccessful shop P(unfavourable | US) was 0.7. What is the EVSI of the information provided by the study? a. b. c. d. Question 2 Assume that the probability that a woman of age 40 in a given population has breast cancer (the prevalence of breast cancer) is 0.5%. The probability that the disease is detected by a mammogram (the sensitivity of the mammogram) is 80%. The...