BFIN 316
Block 3 Warm-up Problems:
Modelling processes and running simulations.
1.The following problem generated a fair amount of controversy a few years ago:
You are a contestant on "Let's Make a Deal." The host tells you that behind one of three curtains is a $10,000 prize; behind the other two curtains there is nothing. You have to choose a curtain. After you do so, the host does NOT open the curtain you chose, but, instead opens one of the curtains you did NOT choose. The curtain that is opened will always be one of the curtains with no prize. So, now there are two curtains left, one of which has the prize. The host now asks you if you wish to change your choice from the curtain you originally chose to the other unopened curtain. Should you switch or stay with your original choice, or does it matter? Simulate this "game" to estimate the probability of winning the prize if you switch, and the probability of winning if you do not switch.
2.Star-crossed soap opera lovers Noah and Julia have had a big argument. Julia's sister, Maria, wants Noah and Julia to make up, so she has told them both to go to the romantic gazebo at 1 p.m. Unfortunately, neither Noah nor Julia are punctual. Each is independently likely to show up at the gazebo any time between 1 and 2 p.m. How long will each have to wait for the other in order for there to be a 75% chance that they will meet? How long would they have to wait to insure a 50% chance that they will meet?
3.Six months before its annual convention, the American Medical Association must determine how many rooms to reserve. At this time the AMA can reserve rooms at a cost of $50 per room. The AMA must pay the $50 room cost even if the room is not occupied. The AMA believes that the number of doctors attending the convention will be normally distributed with a mean of 5000 and a standard deviation of 1000 (but in no event do they expect less than 2500 or more than 10,000 attendees). If the number of people attending the convention exceeds the number of rooms reserved, extra rooms must be paid for at a cost of $80 per room. Use simulation to determine the number of rooms that should be reserved to minimize the expected cost to the AMA