Jane Street–styleTraderAssistant TraderQuestion #200
A seller is offering you a car whose value is uniformly distributed between 0 and 1000, but you do not know the real value and must bid for the car. If your bid is higher than the car's actual value, you buy the car at your bid price and can then resell it elsewhere for 1.5 times its real value. Otherwise, the transaction does not occur. You can only bid once. What is your optimal bid price?
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More Jane Street–Style Trader Questions
A car has a uniformly distributed value between 0 and 1000. If you bid less than this value, you get nothing but keep your bid. If you bid more than this value, you can sell the car for 1.5 times the value. What should you bid? The surface of a 3x3 block is painted. The block is split into 27 cubes and one is dropped on the floor. What is the probability that no visible face is painted? If no visible face is painted, what is the probability that it is the center cube?You flip 4 fair coins and receive $1 for each coin that lands heads. What is the expected value of your total winnings?If you roll two dice, and you have the option to roll again and get paid the highest roll, when is it optimal to reroll?What is 2,000,000 minus 2,022?How many digits does 99 raised to the 99th power have?
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