Jane Street–styleTraderQuantitative TraderQuestion #78
You are presented with three games and must decide which one to play: 1) Throw a standard die and take the square of the resulting value as your score. 2) Throw two dice and take the product of the results as your score. 3) Throw five dice and take the square of the mode of the results as your score. Which game should you choose to maximize your expected payoff?
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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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