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A seller is selling you a car whose value is uniformly distributed between 0 and 1000 but you don’t know the real value and you need to bid for the car. If your bid price is higher than the its real value, the deal will be done at your bid price and you can afterwards resell the car elsewhere for 1.5 times its real value. Otherwise, the deal will not be done. You can only bid once. What will be your optimal bid price?
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Assistant Trader

Interviewed at Jane Street

4.4
Feb 16, 2014

A seller is selling you a car whose value is uniformly distributed between 0 and 1000 but you don’t know the real value and you need to bid for the car. If your bid price is higher than the its real value, the deal will be done at your bid price and you can afterwards resell the car elsewhere for 1.5 times its real value. Otherwise, the deal will not be done. You can only bid once. What will be your optimal bid price?

There exists a six-sided die. The die is rolled. You are paid $x if the die shows x dots (e.g. if you roll 3, then you are paid $3). What is a fair price for this game? Additional layer: after rolling the die once, you have the option of taking the rolled amount or rolling again. However, if you roll again, then you must take the amount corresponding to the second roll. What is a fair price for this game?
avatar

Assistant Trader

Interviewed at Jane Street

4.4
Mar 9, 2010

There exists a six-sided die. The die is rolled. You are paid $x if the die shows x dots (e.g. if you roll 3, then you are paid $3). What is a fair price for this game? Additional layer: after rolling the die once, you have the option of taking the rolled amount or rolling again. However, if you roll again, then you must take the amount corresponding to the second roll. What is a fair price for this game?

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