2 people make bids from 1 to 100. The highest bid is reduced by 10. What should be your strategy to maximise your probability of winning the auciton?
Analyste Quantitative Junior Interview Questions
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Various betting games and confidence intervals
Don't remember but something to do with the speed of an escalator.
Games involving market making on different combinations of dice roll and cards
actions in a game. The die starts with upface 1. The two options you can perform are to roll and to take. Performing a roll re-rolls the current upface of the die. Performing a take allows you to cash out the current upface of the die. Note that the game does not end when you perform a take and that you do not have to roll between takes. Therefore, for example, you can just perform 100 takes on the initial $1 upface and walk away with $100 guaranteed. Your strategy is to cash out the upface when you roll at least some threshold n for the first time. You fix this n at the beginning of the game. Assuming rational strategy in selecting n, what is your expected payout on this game?
Why do you apply to Jane Street ?
Basic probability questions such as expected value, conditional probability.
One 20-sided dice, one 30-sided dice. Roll them both. Expected payoff
Suppose you have two urns that are indistinguishable from the outside. One of the urns contains 3 one-dollar coins and 7 ten-dollar coins. The other urn contains 5 one-dollar coins and 5 ten-dollar coins. Suppose you choose an urn at random and draw a coin from it at random. You find that it is a $10 coin. Now you are given the option to draw again (without replacing the first coin) from either the same urn or the other urn. Should you draw from the same urn or switch
Some Lasso problems that can be view from both ML or optimization perspective
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