Flip a coin four times. If you at first flip a head, you win $1. If you flip a consecutive head, you win double your previous winnings. What is the expected value of your winnings?
Assistants Interview Questions
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You have a box filled with cash. Cash value is uniformly randomly distributed from 1 to 1000. You are trying to win the box in an auction: you win the box if you bid at least the value of the cash in the box; you win nothing if you bid less (but you lose nothing). If you win the box, you can resell it for 150% of its value. How much should you bid to maximize the expected value of your profit (resale of box minus bid)?
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