Jane Street–styleTraderQuantitative TraderQuestion #162
You are waiting for a bus which takes a round trip of 10 minutes to complete (starting again when it finishes one tour). What is your expected waiting time if you arrive at a random time (uniformly from 0 to 10 minutes)? Next, consider that there is an ice cream shop somewhere on the bus route; every time the bus passes it, the driver flips a fair coin and, if heads, spends 10 minutes eating ice cream before continuing the tour. What is your expected waiting time now? How does the answer change if the coin is biased?
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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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