The marketing department of a soft drink company wishes to determine the maximum expected payoff from introducing a new crystal-clear drink. The department considers two investment levels ("Low" and "High") to choose between and regards market share as the key uncertainty that determines ultimate payoffs. These payoffs, depending on the choice of investment level and possible market share, are given in the table below. Investment Level Low High < 1% 300,000 -300,000 ANSWER: WORK: Market Share 1%-4% 400,000 300,000 > 4% 450,000 2,000,000 a) Which investment level should the marketing department choose if they are extremely optimistic about the market share? ANSWER: WORK: b) Which investment level should the marketing department choose if they want to minimize maximum regret?

Suppose you sample one value from a uniform distribution with a = 0 and b=20. a. What is the probability that the value will be between 12 and 172 b. What is the probability that the value will be between 4 and 72 c. What is the mean? d. What is the standard deviation? a. The probability that the value will be between 12 and 17 is (Type an integer or a decimal)

At the beginning of each day, a patient in the hospital is classifed into one of the three conditions: good, fair or critical. At the beginning of the next day, the patient will either still be in the hospital and be in good, fair or critical condition or will be discharged in one of three conditions: improved, unimproved, or dead. The transistion probabilities for this situation are                                         Good    Fair    Critical                        Good         0.65     0.20    0.05                        Fair            0.50     0.30     0.12                        Critical       0.51     0.25     0.20               Improved       Unimproved         Dead Good       0.06               0.03                    0.01 Fair          0.03               0.02                    0.03 Critical     0.01               0.01                    0.02   For example a patient who begins the day in fair condition has a 12% chance of being in critical condition the next day and a 3%…

Suppose that you have two four-sided dice that are each equally weighted (i.e. equal chance of any of the four sides landing face up). One of them has values [12.5968, 2, -2 and -12.5968] , the other [12.5968, 4, -2 and -12.5968] Which of them has a σ of 9 using the probability model approach.   a) [12.5968, 2, -2 and -12.5968]   B) [12.5968, 4, -2 and -12.5968]