Two Sigma Quant Interview Questions
Two Sigma's quant-researcher and engineering interviews lean on probability, statistics, and data-structures-and-algorithms, with an emphasis on rigorous, model-driven thinking.
158 questions tagged to Two Sigma · 28 free to practise now.
- Bond price vs. yieldEasyFinance & DerivativesView →
- Derivative of ln(ln x) at x = eEasyCalculusView →
- Determinant from the spectrumEasyLinear AlgebraView →
- Determinant of a 2×2 (geometry)EasyLinear AlgebraView →
- Determinant of a productEasyLinear AlgebraView →
- Eigenvalue of a matrix powerEasyLinear AlgebraView →
- Even-size subsetEasyProbabilityCombinatoricsView →
- Fixed points of a shuffleEasyCombinatoricsExpected ValueView →
- Hash table average lookupEasyProgramming & DSAView →
- Horner's methodEasyProgramming & DSAView →
- Inverse of a 2×2EasyLinear AlgebraView →
- Matching a specific birthdayEasyProbabilityView →
- Maximum subarray sumEasyProgramming & DSAView →
- Precision of the sample meanEasyRandom VariablesStatisticsView →
- Sharpe ratioEasyStatisticsFinance & DerivativesView →
- Spectrum of a triangular matrixEasyLinear AlgebraView →
- Swap without a tempEasyProgramming & DSAView →
- The 68–95–99.7 ruleEasyStatisticsView →
- Trace from the spectrumEasyLinear AlgebraView →
- Two-sum existenceEasyProgramming & DSAView →
- 25 horses, 5 tracksMediumBrainteasersView →
- All six faces (coupon collector)MediumRandom VariablesExpected ValueView →
- Anagrams of MISSISSIPPIMediumCombinatoricsView →
- Bayes: did it rain?MediumConditional Probability & ExpectationStatisticsView →
- Disease test (Bayes)MediumConditional Probability & ExpectationStatisticsView →
- One hundred light bulbsMediumBrainteasersView →
- Trailing zeros of 100!MediumCombinatoricsView →
- Variance of a dieMediumRandom VariablesStatisticsView →
- Arc-length integral formulaMediumCalculus Premium
- Attributing a superposed Poisson eventMediumProbabilityStochastic Processes Premium
- Average salary, kept privateMediumBrainteasersStatistics Premium
- Best linear blend of two estimatesMediumRandom VariablesStatistics Premium
- Brownian motion propertiesMediumStochastic Processes Premium
- CAPM expected returnMediumStatisticsFinance & Derivatives Premium
- Classify critical points of x^3 - 3xMediumCalculus Premium
- Committee with a chairMediumCombinatorics Premium
- Condition numberMediumLinear Algebra Premium
- Continuously compounded growthMediumFinance & Derivatives Premium
- Convexity correction signMediumFinance & Derivatives Premium
- Covariance of sum and differenceMediumRandom VariablesStatistics Premium
- Density of a sum of two uniformsMediumProbabilityRandom Variables Premium
- Derivative of xˣMediumCalculus Premium
- Determinant of an orthogonal matrixMediumLinear Algebra Premium
- Direction of fastest increaseMediumLinear AlgebraCalculus Premium
- Distinct faces in three rollsMediumExpected Value Premium
- E[X | X > 0] for a standard normalMediumStatisticsCalculus Premium
- Eigenvalues of a 2×2MediumLinear Algebra Premium
- Eigenvalues of a projectionMediumLinear Algebra Premium
- Eigenvalues of a rotationMediumLinear Algebra Premium
- Expected return time from stationary probabilityMediumStochastic Processes Premium
- Fast FibonacciMediumProgramming & DSA Premium
- First passage to ±1MediumStochastic Processes Premium
- Forward vs. futures priceMediumFinance & Derivatives Premium
- Fourth moment of a normalMediumProbabilityRandom Variables Premium
- Fox, goose, beans crossingMediumBrainteasers Premium
- GCD by EuclidMediumProgramming & DSA Premium
- Gap between two uniformsMediumExpected ValueStatistics Premium
- Guess 2/3 of the averageMediumMarket Making & Betting Games Premium
- Identify the sortMediumProgramming & DSA Premium
- Kelly sizingMediumMarket Making & Betting Games Premium
- LU vs. CholeskyMediumLinear Algebra Premium
- Letters into envelopesMediumProbabilityExpected Value Premium
- MGF of an exponentialMediumRandom VariablesCalculus Premium
- Macaulay duration of a zeroMediumFinance & Derivatives Premium
- Mean of a lognormalMediumRandom VariablesFinance & Derivatives Premium
- Mean value theorem for x^2MediumCalculus Premium
- Median of an exponentialMediumRandom VariablesStatistics Premium
- Memoryless waitingMediumConditional Probability & ExpectationRandom Variables Premium
- Minimum of three uniformsMediumProbabilityRandom Variables Premium
- Minimum-variance weightsMediumStatisticsFinance & Derivatives Premium
- Monte Carlo variance reductionMediumFinance & DerivativesProgramming & DSA Premium
- Non-attacking rooksMediumCombinatorics Premium
- One step of Newton's methodMediumCalculus Premium
- Onto functionsMediumCombinatorics Premium
- Particular solution of an ODEMediumCalculus Premium
- Poisson inter-arrivalsMediumProbabilityStochastic Processes Premium
- Positive definite matricesMediumLinear Algebra Premium
- Positive semidefinitenessMediumStatisticsLinear Algebra Premium
- Power iterationMediumLinear AlgebraProgramming & DSA Premium
- Power of three in a factorialMediumCombinatorics Premium
- Projecting onto a lineMediumLinear Algebra Premium
- QR decompositionMediumLinear Algebra Premium
- Quickselect average complexityMediumProgramming & DSA Premium
- Rank–nullityMediumLinear Algebra Premium
- Regression to the meanMediumBrainteasersStatistics Premium
- Renewal-reward fraction of time runningMediumExpected ValueStochastic Processes Premium
- Sampling an exponential from a uniformMediumRandom VariablesProgramming & DSA Premium
- Second-price auction strategyMediumProbabilityMarket Making & Betting Games Premium
- Shape of the normalMediumRandom VariablesStatistics Premium
- Short-rate modelsMediumStochastic ProcessesFinance & Derivatives Premium
- Slope of a regression lineMediumStatisticsLinear Algebra Premium
- Spam filterMediumProbabilityConditional Probability & Expectation Premium
- Spectrum of a symmetric matrixMediumStatisticsLinear Algebra Premium
- Splitting a known sumMediumConditional Probability & ExpectationExpected Value Premium
- Standard error of a proportionMediumRandom VariablesStatistics Premium
- Stationary distribution of a two-state chainMediumProbabilityStochastic Processes Premium
- Subsets with no neighborsMediumCombinatorics Premium
- Sum of squared standard normalsMediumRandom VariablesStatistics Premium
- The Gaussian integralMediumCalculus Premium
- The cab problemMediumProbabilityConditional Probability & Expectation Premium
- Trace of a productMediumLinear Algebra Premium
- Uncorrelated but dependentMediumRandom VariablesStatistics Premium
- Uniform random permutationMediumProgramming & DSA Premium
- Variance-minimizing hedgeMediumProbabilityStatistics Premium
- Why covariance matrices are PSDMediumStatisticsLinear Algebra Premium
- Will they meet?MediumProbability Premium
- k-th order statisticMediumExpected ValueStatistics Premium
- x^4 coefficient of the Maclaurin series of e^xMediumCalculus Premium
- A 12 before two 7sHardProbabilityStochastic Processes Premium
- A divergent reciprocal expectationHardRandom VariablesCalculus Premium
- Ages from product and sumHardCombinatoricsBrainteasers Premium
- Amoeba extinctionHardProbabilityStochastic Processes Premium
- Balanced parenthesesHardCombinatoricsProgramming & DSA Premium
- Bertrand's chordHardProbabilityBrainteasers Premium
- Blue-eyed islandersHardBrainteasers Premium
- Branching process extinction (supercritical)HardProbabilityStochastic Processes Premium
- Broken-stick triangleHardProbability Premium
- Buffon's needleHardProbabilityCalculus Premium
- Cayley–Hamilton theoremHardLinear Algebra Premium
- Correlation of min and maxHardProbabilityRandom Variables Premium
- Covariance of multinomial countsHardRandom VariablesStatistics Premium
- Cycles in a shuffleHardCombinatoricsExpected Value Premium
- Draws until a smaller valueHardExpected Value Premium
- Dynamic programming: coin changeHardProgramming & DSA Premium
- Ehrenfest urn stationary distributionHardProbabilityStochastic Processes Premium
- Expected duration of a fair walkHardExpected ValueStochastic Processes Premium
- Expected flips for HHHardRandom VariablesExpected Value Premium
- Expected visits before absorptionHardExpected ValueStochastic Processes Premium
- Finite-difference stabilityHardFinance & DerivativesProgramming & DSA Premium
- Floating-point summation errorHardCalculusProgramming & DSA Premium
- Gambler's ruinHardProbabilityStochastic Processes Premium
- Handshakes at a dinner partyHardCombinatoricsBrainteasers Premium
- Hats with 100 colorsHardBrainteasers Premium
- Itô drift of W squaredHardCalculusStochastic Processes Premium
- Laplace's rule of successionHardProbabilityConditional Probability & Expectation Premium
- Making change in lineHardCombinatoricsStochastic Processes Premium
- Meaning of N(d₂)HardFinance & Derivatives Premium
- Median of a streamHardStatisticsProgramming & DSA Premium
- Newton's method convergenceHardCalculusProgramming & DSA Premium
- Optional stopping between +3 and −5HardExpected ValueStochastic Processes Premium
- Order statistics are BetaHardRandom VariablesStatistics Premium
- Pricing an inverse floaterHardFinance & Derivatives Premium
- Prisoners and the boxesHardProbabilityBrainteasers Premium
- Quadratic variation of Brownian motionHardCalculusStochastic Processes Premium
- Reflection principle for the maximumHardProbabilityStochastic Processes Premium
- Repainting balls to one colorHardExpected ValueStochastic Processes Premium
- Reservoir samplingHardStatisticsProgramming & DSA Premium
- Risk-neutral up probabilityHardStochastic ProcessesFinance & Derivatives Premium
- Singular values via AᵀAHardLinear Algebra Premium
- The drunk passengerHardProbabilityConditional Probability & Expectation Premium
- The racing camelsHardBrainteasers Premium
- The two-envelopes paradoxHardProbabilityConditional Probability & Expectation Premium
- Triangle from three independent sticksHardProbabilityCalculus Premium
- Two eggs, 100 floorsHardBrainteasers Premium
- Two positive testsHardProbabilityConditional Probability & Expectation Premium
- Two-color necklacesHardCombinatorics Premium
- Uniforms summing past 1HardRandom VariablesExpected Value Premium
- Value of the Basel sumHardCalculus Premium
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