Honor Code: You must do these problems on your own, and submit your answers no later than 11 PM on Sunday, December 2.
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Your company, Extreme Sports Unlimited Ltd, is facing a class action suit which charges that ESU's "Death Frisbee" is responsible for injuries incurred by several purchasers.
Your corporate lawyers had written a tight waiver of responsibility, which is prominently displayed on the outside of every package. As a result, your civil attorneys estimate a 65% chance that you'll prevail in the lawsuit (i.e., be found "not liable" by the jury).
The plaintiffs have offered to settle the suit for $750,000. Your attorneys have presented you with three alternatives: Settle, go immediately to trial, or withhold your settle-vs-trial decision until after a mock trial has been conducted.
The mock trial would involve hiring a retired judge and 12 citizens (as a mock jury), quickly presenting your case (and that of the plaintiffs), and asking the jury to render a "liable" or "not liable" decision. From prior experience, the attorneys tell you that mock juries rule the same way real juries would (with respect to either finding) about 75% of the time.
It would cost $50,000 (including legal fees) to hold the mock trial. Your attorneys have estimated that a real trial will cost $200,000 in additional legal fees (whether the mock trial is held or not), and a finding of liability will cost you $2,000,000 in payment to the plaintiffs (and their attorneys).
Should you settle immediately, go to trial immediately, or wait and hold a mock trial first? If you hold a mock trial, how should the outcome affect your final settle-or-go-to-trial decision?
What is ESU's optimal strategy?
Following your optimal strategy, what is ESU's expected overall cost? $
Hint: The decision tree for this problem has very much the same structure as the decision tree for Leon's cub-purchase problem.
Freddie "the Falcon" is preparing for his last jump in the Winter Olympics K120 Individual Ski-Jumping competition. He has a choice: Go "all-out," or jump conservatively.
He figures that he needs a jump of at least 130 meters in order to win a medal. (He doesn't care which medal he wins - His endorsement contract with ESU will be renewed as long as he wins one of the medals.)
An all-out jump has a 35% chance of ending in a fall, and disqualification. But if he lands successfully, the length of the jump will be normally distributed, with an expected length of 132 meters, and a standard deviation of 8 meters. If he jumps conservatively, he'll surely land successfully, but with an expected length of only 129 meters, and a standard deviation of 3 meters.
What is Freddie's chance of medaling if he jumps conservatively? %
What is Freddie's chance of medaling if he jumps all-out? %
Actually, the 130-meters-to-medal requirement is only an estimate (since several jumpers will do their last jumps after him): One standard-deviation's-worth of (normally-distributed) uncertainty in this estimate is 3 meters. Use 20,000 simulated observations of the medaling requirement, a conservative jump, and an all-out jump to estimate Freddie's chance of winning if he jumps conservatively, and if he jumps all-out.
Probability of medaling with a conservative jump: %
Probability of medaling with an all-out jump: %
In a post-competition exhibition, Freddie does two conservative jumps. Using 20,000 simulated observations, estimate the expected length of the longer of the two jumps. meters
Roughly how many observations would be needed to make this estimate with a margin of error (at the 95%-confidence level) of only 1 centimeter (0.01 meters)? observations
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