Quant interview preparation

Prop market making and quantitative research, weighted the way the interviews actually are: probability and expected value, statistics and machine learning, market making logic, programming and options. Every question is either traced to a named firm from a public candidate report, or tagged at desk level when we could not trace it, and every probability answer shows the reasoning path rather than just the number.

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Question bank

100 questions, mapped to the firms that asked them

Questions
100
Traced to a firm
53
Firms
15
Updated
September 2026
Asked at
All firmsOld Mission Capital12Tower Research Capital10Jump Trading7Akuna Capital5Citadel4D.E. Shaw3Jane Street3AQR Capital Management2DRW2Millennium Management2Schonfeld2Squarepoint Capital2Susquehanna International Group2Belvedere Trading1Optiver1
Topic
All topicsProbability10Coins, cards and games6Expected value8Statistics11Market making15Estimation and mental maths4Stochastic processes4Regression5Machine learning6Time series6Programming10Options and derivatives8Fit and motivation7
Level
AnyCoreIntermediateHard
Type
AnyBrainteaserTechnicalCaseMarket viewFit
Showing 1–1 of 1 · filtered from 100Clear filters
  1. 008What is the expected value of a roll of a fair six-sided die?Expected valueCorephone / first roundOld Mission CapitalTrading · Chicago · 2020

    Say this

    Three and a half. Each face has probability one sixth, and one through six sums to 21, so 21 over 6 is 3.5. Or faster: for a uniform run of integers the mean is the midpoint, which is (1 plus 6) over 2.

    Then walk it

    1. The sum one to n is n(n+1)/2, so the mean of a uniform die with n faces is (n+1)/2. For six faces that is 3.5.
    2. Variance is worth having ready too, because it is the immediate follow-up. E of X squared is (1+4+9+16+25+36)/6, which is 91/6, about 15.17. Subtract 3.5 squared, 12.25, and you get 35/12, about 2.917. Standard deviation is about 1.71.
    3. Also useful to know the general formula: the variance of a uniform die with n faces is (n squared minus 1) over 12. For n equal to 6 that is 35/12, matching.
    4. Two dice: expected sum is 7 by linearity, and variance is 35/6 because they are independent, so standard deviation is about 2.42.
    5. The reason a trading desk opens with this is speed and composure, not difficulty. Answer in under two seconds and have the variance ready before they ask, because the real question is the next one.

    Where candidates lose it

    Hesitating. This is a warm-up and any pause reads badly. The second trap is being caught flat-footed on variance, which follows more than half the time. Know 35/12 and know that the standard deviation of a die is about 1.71.

    Expect next

    • What is the variance?
    • What about the sum of two dice?
    • What is the expected value of the maximum of two dice?

    Reported by candidates at Old Mission Capital (Trading, Chicago, 2020). Source: Wall Street Oasis.

Firm tags come from public, anonymous candidate reports on Wall Street Oasis: strong signal, not sworn testimony. Firms are named as the places a question was reported, not as partners of Fin Maverick. Answers are written for this page to show how to think out loud; they are not scripts to recite.