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.

Jump to the question bank
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. 011A random variable is uniform on the interval zero to ten. What are its expected value and variance?StatisticsCorephone / first roundOld Mission CapitalFinance · New York · 2018

    Say this

    Mean 5, variance 100 over 12, which is 8.33, so standard deviation about 2.89. For a uniform on a to b the mean is the midpoint and the variance is (b minus a) squared over 12.

    Then walk it

    1. Mean by symmetry: the midpoint of 0 and 10 is 5. No integration needed.
    2. Variance from the formula (b-a) squared over 12: 100 over 12 equals 8.33, standard deviation 2.887.
    3. If you want to derive it, E of X squared is the integral of x squared over 10 from 0 to 10, which is 1000/30 equals 33.33. Subtract 25 and you get 8.33. Good to be able to do it either way.
    4. The 1/12 is worth carrying in your head because it recurs: a fair n-sided die has variance (n squared minus 1)/12, and the rounding error of a value rounded to the nearest tick has variance tick squared over 12. That last one comes up in real microstructure work.
    5. Practical note: the uniform has thin support and no tails, so it is a bad default for anything financial. The moment somebody hands you a uniform in a trading context, ask what it is meant to represent.

    Where candidates lose it

    Reaching for integration under time pressure and fumbling the arithmetic. Know the (b-a) squared over 12 form cold. Also do not quote variance when they asked for standard deviation or the other way round, and say which one you are giving.

    Expect next

    • What is the expected value of the maximum of two independent draws?
    • What is the distribution of the sum of two independent uniforms?
    • What is the variance of the rounding error when you round to the nearest penny?

    Reported by candidates at Old Mission Capital (Finance, New York, 2018). 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.