Quant interview preparation

Questions

100

Traced to a firm

53

Firms

15

Updated

September 2026

Asked at

All firmsOld Mission Capital12Tower Research Capital10Jump Trading7Akuna Capital5Citadel4DED.E. Shaw3Jane Street3ACAQR Capital Management2DRW2Millennium Management2Schonfeld2SCSquarepoint Capital2Susquehanna International Group2Belvedere Trading1Optiver1

Topic

All topicsProbability10Coins, cards and games6Expected value8Statistics11Market making15Estimation and mental maths4Stochastic processes4Regression5Machine learning6Time series6Programming10Options and derivatives8Fit and motivation7

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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.

2. 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.