some probability questions
Quantitative Trader Interview Questions
1,133 quantitative trader interview questions shared by candidates
Solving the Blotto puzzle and market making questions.
Expected value, statistics, dice problems
Probability and expected value questions.
The phone interviewer asked me two brainteaser/probability questions. One was a typical probability of picking a matching pair of socks if you have a certain number of similar socks in a drawer.
On an elevator and 2 other people enter expected value of the number of times the elevator stops
1. What is the expectation of the product of two die rolls? 2. Instead of die imagine drawing cards with the same numbers written on the cards but without replacement, is the expected value of the product smaller/larger/the same comparing to 1? 3. You can split the deck of cards from 2 into two piles. Then you draw a random card form the first and the second piles and compute the product of numbers written on the two cards. How do you split the deck to maximize the expectation of the product? 4. Some other game that involves 10 cakes with 9 being of one flavor, and one being of a different flavor, and the task is to guess correctly as many flavors as you can, but I don't remember the exact rules.
Classic questions about rolling dice, questions about conditional probability, questions about pulling cards from a deck
Bid on sum of 2 dice
Great news! The variety of robotic competition continues to grow at breakneck pace! Most recently, head-to-head long jump contests have been all the rage. These contests consist of rounds in which each robot has a single attempt to score. In an attempt, a robot speeds down the running track (modeled as the numberline) from 0, the starting line, to 1, the takeoff point. A robot moves along this track by drawing a real number uniformly from [0,1] and adding it to the robot’s current position. After each of these advances, the robot must decide whether to jump or wait. If a robot crosses the takeoff point (at 1) before jumping its attempt receives a score of 0. If the robot jumps before crossing 1, it draws one final real number from [0,1] and adds it to its current position, and this final sum is the score of the attempt. In a head-to-head contest, the two robots each have a single attempt without knowing the other’s result. In the case that they tie (typically because they both scored 0), that round is discarded and a new round begins. As soon as one robot scores higher than the other on the same round, that robot is declared the winner! Assume both robots are programmed to optimize their probability of winning and are aware of each other’s strategies. You are just sitting down to watch a match’s very first attempt (of the first round, which may or may not end up being discarded). What is the probability that this attempt scores 0?
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