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Quantitative researcher Interview Questions

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First round: basic probability, combinatorics. A bear wants to catch 3 fish from a river. when he has caught 3 fish, he'll leave. when a fish comes, there is a 1/2 chance he'll catch it. what's the probability that the 5th fish will not be caught?

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P: The 5th fish has been caught, P=P1+P2+P2, where, P1: The 5th fish been caught as the first one P2: ... second one... P3: ....third one (or the last one). P1 = 0.5^5 P2 = 4*0.5^5 P3 = 6*0.5^5 The fifth fish will not be caught Pc = 1-P = 1-P1-P2-P3

I got a different answer :/ There's 2 ways the fish can survive: either the bear leaves before the 5th fish, or the bear fails to catch it. The probability the bear leaves is the probability the bear gets 3 fish in 4 attempts, or 4C3/16 = 1/4 The probability the bear tries * fails to catch the fish is 3/4 (the probability of trying) * 1/2 (the probability of failing) = 3/8. The total probability is thus 5/8? Not sure what I did differently

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given a series of stock prices, describe an algorithm to find the best buy and sell point. ( only one buy and one sell, buy before sell)

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throwing a dice until the face 6 comes up two times, what is the expected stopping time

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I met a coule of quants with average MSc degrees from average schools, sub-par work experiences but with egos of Nobel Prize winners. I was very surprised to see the mediocrity of these two quants because I had read that GSA had only recruited 25 profiles out of 10000 in the last few years so I was expecting people working there to be Quants from the top 10 schools with Quantitative PhDs (which is my case). The recruiter had mentioned to me prior the interview that GSA looked as much at personality fit than skills so I was really on my best behaviour and within the Quant community I am usually known to be pleasant and easy to work with. However, both of these interviewers had severe personal issues. The first one wouldn't tell me about his background because "he was the one asking the questions" and the second thought that a multi linear regression (MLR) was the best Machine Learning Techniques and would scowl at me when I would confront him with the fact that the assumptions behind an MLR around returns being i.i.d were violated by the observed data and that as a result taking a Bayesian approach had more potential in my opinion. As a result of giving my honest opinion and seing through his facial expression the kind of tantrum anger you see on pre-adolescent children, he then went on a rampage trying to make me fail in his next few questions which I answered correctly but instead of moving on to the next ones quickly, he tried to make me fail with stupid details instead of help me show my best through asking additional conceptual questions and bringing the conversation to an interesting level of abstraction in which interesting trading ideas could emerge. I lost interest in GSA as a result of these interviews (GSA was amongst my top 10 preferred places to work for before that). It's a shame. I don't understand why management decided to put these two clowns as the face of GSA. They really give a poor image of the company. Currently, my best offers are with Goldman Sachs and the Man Group. It would have been good to be able to compare an offer with GSA.

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If I break a stick of unit length into three random pieces, what’s the expected length of the largest piece?

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Why did you leave the job before your last job.

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Pseudocode to calculate standard deviation. How would you optimize it? Where might it go wrong?

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lots of probability and statistics.

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tricky calculus questions, whiteboard code to do with trees.

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The assignment was on a weather dataset containing hourly observations from weather stations in London and Paris. The first question was: "Give an example of a serie that follows a normal/gaussian distribution. Describe it and re-normalize. Give an example of a serie that is not normal/gaussian and normalise it."

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