Data-Driven Research Interview Questions
Data-driven research interviews are collaborative and open-ended: probability and statistics, analysis on a provided dataset, and coding, with an emphasis on rigorous model-driven thinking.
Expect open-ended, data-driven problems: probability and statistics, data analysis on a provided dataset, and coding and algorithms. The work ranges from simple statistics to machine learning, and interviews reward how you reason through a problem over what you can recall.
Interviews in this format are typically conducted over video and are deliberately collaborative - you are encouraged to stop and think, and interviewers will offer hints. An automated technical assessment usually comes first, with Python the common language.
315 questions tagged to Data-Driven Research · 192 free to practise now.
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This format weights probability, statistics, and programming. Strengthen all three with:
- A coin that branches into a dieEasyCombinatoricsExpected ValueView →
- A race between two small-angle ratesEasyCalculusView →
- All the squares on a chessboardEasyCombinatoricsBrainteasersView →
- An even palindromeEasyProbabilityCombinatoricsView →
- Angle under an orthogonal mapEasyLinear AlgebraView →
- Correlation under rescalingEasyRandom VariablesStatisticsView →
- Counting complement pairsEasyProgramming & DSAView →
- Covariance of a chi-square and a ratioEasyRandom VariablesStatisticsView →
- Covariance of summed Brownian motionsEasyStochastic ProcessesView →
- Determinant after antisymmetrizingEasyProbabilityLinear AlgebraView →
- Determinant from trace and one eigenvalueEasyLinear AlgebraView →
- Determinant of a scaled productEasyLinear AlgebraView →
- Diagonal parameter from a triangular determinantEasyLinear AlgebraView →
- Eigenvalues of a 2×2 matrixEasyLinear AlgebraView →
- Even numbers, distinct digitsEasyCombinatoricsView →
- Even-size, non-empty subsetEasyProbabilityCombinatoricsView →
- Exactly one clears two-thirdsEasyProbabilityRandom VariablesView →
- Expected cost of a mixed lookup workloadEasyProgramming & DSAView →
- How many new hires to lift the averageEasyStatisticsView →
- Interquartile range of an exponentialEasyRandom VariablesStatisticsView →
- Largest eigenvalue after squaringEasyLinear AlgebraView →
- Largest possible covarianceEasyRandom VariablesStatisticsView →
- MISSISSIPPI with the P's togetherEasyCombinatoricsView →
- Maximum of four uniforms in a bandEasyProbabilityRandom VariablesView →
- Maximum subarray sumEasyProgramming & DSAView →
- Multiplications saved by Horner's methodEasyProgramming & DSAView →
- No heads in a random number of flipsEasyProbabilityRandom VariablesView →
- Norm after imposing orthogonalityEasyLinear AlgebraView →
- Parameter values for a singular matrixEasyLinear AlgebraView →
- Pooling two independent estimatesEasyRandom VariablesStatisticsView →
- Posterior from a likelihood ratioEasyConditional Probability & ExpectationStatisticsView →
- R-squared from the sums of squaresEasyStatisticsView →
- R-squared when you duplicate every pointEasyStatisticsView →
- Recover an XOR of two unknownsEasyProgramming & DSAView →
- Regressing with zero covarianceEasyRandom VariablesStatisticsView →
- Repricing a bond after a yield jumpEasyFinance & DerivativesView →
- Sample SD with Bessel's correctionEasyStatisticsView →
- Second moment from varianceEasyRandom VariablesStatisticsView →
- Sharing your weekday of birthEasyProbabilityView →
- Sharpe of two combined uncorrelated strategiesEasyStatisticsFinance & DerivativesView →
- Skewness of a Laplace variableEasyRandom VariablesStatisticsView →
- Standard deviation of a correlated sumEasyRandom VariablesStatisticsView →
- Strictly increasing three-digit numbersEasyCombinatoricsView →
- Sum of cubed eigenvaluesEasyLinear AlgebraView →
- Sum of the OLS coefficientsEasyStatisticsView →
- Three-one strings with matching endpointsEasyCombinatoricsView →
- Two ordering constraints at onceEasyProbabilityCombinatoricsView →
- Upper bound on a dry weekendEasyProbabilityView →
- Valuing a level perpetuityEasyFinance & DerivativesView →
- Variance of a sum of Brownian motionEasyStochastic ProcessesView →
- Weighting a fixed sumEasyConditional Probability & ExpectationExpected ValueView →
- Where counting sort places a valueEasyProgramming & DSAView →
- Where the arrivals landEasyProbabilityStochastic ProcessesView →
- Where x squared log x bottoms outEasyCalculusView →
- 25 horses, 5 tracksMediumBrainteasersView →
- A Cholesky diagonal entryMediumLinear AlgebraView →
- A Gram–Schmidt R entryMediumLinear AlgebraView →
- A cube ending in elevenMediumProbabilityBrainteasersView →
- A difference of three normalsMediumRandom VariablesStatisticsView →
- A ratio of gamma valuesMediumRandom VariablesView →
- A tenth power of a matrixMediumLinear AlgebraView →
- All six faces (coupon collector)MediumRandom VariablesExpected ValueView →
- An ant returning to its cornerMediumExpected ValueStochastic ProcessesView →
- Average salary, kept privateMediumBrainteasersStatisticsView →
- Balanced parenthesesMediumCombinatoricsProgramming & DSAView →
- Bayes: did it rain?MediumConditional Probability & ExpectationStatisticsView →
- Best linear blend of two estimatesMediumRandom VariablesStatisticsView →
- Boy–girl neighbors in a lineMediumCombinatoricsExpected ValueView →
- Conditional mean on a circleMediumConditional Probability & ExpectationRandom VariablesView →
- Correlation of two face-countsMediumProbabilityStatisticsView →
- Cosine of a conditional meanMediumProbabilityConditional Probability & ExpectationView →
- Covariance from a triangular densityMediumRandom VariablesStatisticsView →
- Covariance of a Poisson processMediumStochastic ProcessesView →
- Covariance of sum and differenceMediumRandom VariablesStatisticsView →
- Deleting every other number on a circleMediumCombinatoricsBrainteasersView →
- Density of a sum of two uniformsMediumProbabilityRandom VariablesView →
- Derivative of xˣMediumCalculusView →
- Digits of concatenated powersMediumBrainteasersView →
- Disease test (Bayes)MediumConditional Probability & ExpectationStatisticsView →
- Distinct faces in three rollsMediumExpected ValueView →
- E[X | X > 0] for a standard normalMediumStatisticsCalculusView →
- Eigenvalues of a projectionMediumLinear AlgebraView →
- Eigenvalues of a rotationMediumLinear AlgebraView →
- Enlarging a square orchardMediumBrainteasersView →
- Expected flips for HHMediumRandom VariablesExpected ValueView →
- Expected gap between two normalsMediumRandom VariablesView →
- Expected gap on 30-sided diceMediumProbabilityExpected ValueView →
- Expected square of a random unit complex numberMediumProbabilityRandom VariablesView →
- First passage to ±1MediumStochastic ProcessesView →
- Fox, goose, beans crossingMediumBrainteasersView →
- Gambler's ruinMediumProbabilityStochastic ProcessesView →
- Growth rate of a rank-one eigenvalueMediumLinear AlgebraView →
- Guess 2/3 of the averageMediumMarket Making & Betting GamesView →
- How large can the off-diagonal be?MediumLinear AlgebraView →
- How much a control variate helpsMediumFinance & DerivativesProgramming & DSAView →
- Kelly sizing on an asymmetric betMediumMarket Making & Betting GamesView →
- Largest eigenvalue of a rank-one updateMediumLinear AlgebraView →
- Letters into envelopesMediumProbabilityExpected ValueView →
- Log-dynamics of a geometric Brownian motionMediumStochastic ProcessesView →
- Maximum variance on an intervalMediumRandom VariablesStatisticsView →
- Median of a list and its squaresMediumCombinatoricsStatisticsView →
- Minimum-variance weightsMediumStatisticsFinance & DerivativesView →
- Multiplications in fast exponentiationMediumProgramming & DSAView →
- Newton's division-free reciprocalMediumCalculusView →
- No two neighboring bulbs litMediumProbabilityCombinatoricsView →
- Non-attacking rooksMediumCombinatoricsView →
- Norm of a doubly-stochastic stationary vectorMediumLinear AlgebraStochastic ProcessesView →
- One hundred light bulbsMediumBrainteasersView →
- Quicksort's worst case, countedMediumProgramming & DSAView →
- Rank and nullity of a rotationMediumLinear AlgebraView →
- Ratio of partial sumsMediumRandom VariablesExpected ValueView →
- Rebuilding a tower of ten ringsMediumBrainteasersProgramming & DSAView →
- Resonance in undetermined coefficientsMediumCalculusView →
- Sampling an exponential from a uniformMediumRandom VariablesProgramming & DSAView →
- Spectrum of a constant-diagonal matrixMediumLinear AlgebraView →
- Spectrum of a symmetric matrixMediumStatisticsLinear AlgebraView →
- Sum and difference of perfectly correlated variablesMediumRandom VariablesStatisticsView →
- Sum of the pandigital numbersMediumCombinatoricsBrainteasersView →
- Swapping the regression variablesMediumStatisticsView →
- The Gaussian integralMediumCalculusView →
- The German tank problemMediumExpected ValueStatisticsView →
- The last lightbulb to burn outMediumRandom VariablesExpected ValueView →
- The same number of tailsMediumProbabilityCombinatoricsView →
- Trace of a productMediumLinear AlgebraView →
- Trailing zeros of 100!MediumCombinatoricsView →
- Uncorrelated but dependentMediumRandom VariablesStatisticsView →
- Variance of a Brownian combinationMediumStochastic ProcessesView →
- Variance of a time-weighted Itô integralMediumCalculusStochastic ProcessesView →
- Variance of hearts in eight cardsMediumCombinatoricsStatisticsView →
- Variance of integrated Brownian motionMediumStochastic ProcessesView →
- Variance of the larger of two diceMediumRandom VariablesStatisticsView →
- When the naive shuffle is biasedMediumProgramming & DSAView →
- Will they meet?MediumProbabilityView →
- X positive given the sum is positiveMediumProbabilityRandom VariablesView →
- A 12 before two 7sHardProbabilityStochastic ProcessesView →
- A function minus its derivativeHardCalculusView →
- A geometric series that sums to a squareHardBrainteasersView →
- A half-plane, given positiveHardProbabilityRandom VariablesView →
- A rectangle over the shaded rowHardProbabilityCombinatoricsView →
- A weighted sum of binomialsHardCombinatoricsBrainteasersView →
- Average of near-diagonal numbersHardCombinatoricsBrainteasersView →
- Cars advancing to the endHardProbabilityExpected ValueView →
- Conditioning a Brownian bridgeHardStochastic ProcessesView →
- Covariance of X with Y squaredHardRandom VariablesStatisticsView →
- Cuts until one orb remainsHardProbabilityExpected ValueView →
- Digits with distinct pairwise sumsHardCombinatoricsBrainteasersView →
- Distinct toys from seven boxesHardProbabilityExpected ValueView →
- Doors toggled by primesHardCombinatoricsBrainteasersView →
- Draws to beat a hidden uniformHardRandom VariablesExpected ValueView →
- Draws to pass a log thresholdHardProbabilityRandom VariablesView →
- Draws to pass twoHardProbabilityRandom VariablesView →
- Expected arc covering a fixed pointHardProbabilityExpected ValueView →
- Expected largest of ten ballsHardCombinatoricsExpected ValueView →
- Head density with no two in a rowHardProbabilityCombinatoricsView →
- Hitting zero on a ringHardProbabilityStochastic ProcessesView →
- How many long cycles?HardProbabilityCombinatoricsView →
- Locks for a four-of-seven safeHardCombinatoricsBrainteasersView →
- Long cycles in a random permutationHardCombinatoricsExpected ValueView →
- Loops from tying noodlesHardProbabilityExpected ValueView →
- Mean of a mean-reverting processHardStochastic ProcessesFinance & DerivativesView →
- No two samples too closeHardProbabilityCombinatoricsView →
- Odd sums on a 3×3 gridHardProbabilityCombinatoricsView →
- Only seven left unchosenHardProbabilityCombinatoricsView →
- Overshoot past oneHardProbabilityRandom VariablesView →
- Pairing gloves within oneHardProbabilityCombinatoricsView →
- Pairing with a difference of 1 or 11HardCombinatoricsBrainteasersView →
- Penalty kicks with a shifting rateHardProbabilityRandom VariablesView →
- Quadratic variation in mean-squareHardStochastic ProcessesView →
- Range beats the midpointHardProbabilityRandom VariablesView →
- Reading N(d₂) in Black–ScholesHardFinance & DerivativesView →
- Rolls to a six, given all evenHardConditional Probability & ExpectationExpected ValueView →
- Rounds to see all faces with two diceHardProbabilityExpected ValueView →
- Runs of red and blue marblesHardCombinatoricsExpected ValueView →
- Shuffles to restore the deckHardCombinatoricsBrainteasersView →
- Smallest possible MGF valueHardRandom VariablesStatisticsView →
- Spread of a lognormal raised to the fourthHardRandom VariablesStatisticsView →
- Spread of a multinomial count gapHardRandom VariablesStatisticsView →
- Subsets with one consecutive pairHardCombinatoricsView →
- Sum of repeating decimalsHardCombinatoricsBrainteasersView →
- Ten prime digits with a set productHardCombinatoricsView →
- The decreasing run of uniformsHardRandom VariablesExpected ValueView →
- The drunk passengerHardProbabilityConditional Probability & ExpectationView →
- Three eggs, nine dropsHardCombinatoricsBrainteasersView →
- Two Brownian values, both positiveHardProbabilityStochastic ProcessesView →
- Two walks returning togetherHardProbabilityCombinatoricsView →
- Two-color necklacesHardCombinatoricsView →
- Uniforms summing past 1HardRandom VariablesExpected ValueView →
- Variance of an Itô integralHardStochastic ProcessesView →
- Variance of the exponential of a gammaHardRandom VariablesStatisticsView →
- Variance under random parametersHardRandom VariablesStatisticsView →
- When k-to-the-k is a squareHardCombinatoricsBrainteasersView →
- When the extremes sum above oneHardProbabilityRandom VariablesView →
- Two searches, neither hitsEasyRandom Variables Premium
- A CLT tail probabilityMediumStatistics Premium
- A cube root by tangent lineMediumCalculus Premium
- A divergent reciprocal expectationMediumRandom VariablesCalculus Premium
- A mean-reverting processMediumStochastic ProcessesFinance & Derivatives Premium
- A relay team with a feudMediumCombinatorics Premium
- A stationary probabilityMediumStochastic Processes Premium
- A two-step transitionMediumStochastic Processes Premium
- Arbitraging a mispriced forward loanMediumFinance & Derivatives Premium
- Arc length of a curveMediumCalculus Premium
- Arrivals before the rival streamMediumProbabilityStochastic Processes Premium
- Back out the market premium, then price a stockMediumStatisticsFinance & Derivatives Premium
- Classify critical points of x^3 - 3xMediumCalculus Premium
- Condition numberMediumLinear Algebra Premium
- Conditioning Brownian motion on its futureMediumStochastic Processes Premium
- Confidence interval with the right pivotMediumStatistics Premium
- Convexity correction signMediumFinance & Derivatives Premium
- Derangements of four itemsMediumCombinatorics Premium
- Determinant of a 3×3MediumLinear Algebra Premium
- Determinant of a compound expressionMediumLinear Algebra Premium
- Determinant of an orthogonal matrixMediumLinear Algebra Premium
- Distinct faces in five rollsMediumCombinatoricsExpected Value Premium
- Equivalent continuously-compounded rateMediumFinance & Derivatives Premium
- Euclid's worst-case step countMediumProgramming & DSA Premium
- Expected ascents in a shuffleMediumCombinatoricsExpected Value Premium
- Expected sum of a random subsetMediumExpected Value Premium
- Expected value of a mean-reverting processMediumStochastic Processes Premium
- Finite-difference stabilityMediumFinance & DerivativesProgramming & DSA Premium
- Forward vs. futures priceMediumFinance & Derivatives Premium
- Fourth moment of a shifted normalMediumProbabilityRandom Variables Premium
- Gap between two uniformsMediumExpected ValueStatistics Premium
- How explosive is naive Fibonacci?MediumProgramming & DSA Premium
- How fast is the balloon growing?MediumCalculus Premium
- How many trials to poll a proportionMediumRandom VariablesStatistics Premium
- How often the smallest disk movesMediumProgramming & DSA Premium
- Largest pen against a riverMediumCalculus Premium
- Macaulay duration of a coupon bondMediumFinance & Derivatives Premium
- Marking a seasoned forwardMediumFinance & Derivatives Premium
- Maximum rate of increaseMediumLinear AlgebraCalculus Premium
- Mean value theorem for x^2MediumCalculus Premium
- Median of a linear densityMediumRandom VariablesCalculus Premium
- Memoryless waitingMediumConditional Probability & ExpectationRandom Variables Premium
- Minimum-variance portfolio weightMediumStatisticsFinance & Derivatives Premium
- Nullity of a concrete matrixMediumLinear Algebra Premium
- Onto functionsMediumCombinatorics Premium
- Positive semidefinitenessMediumStatisticsLinear Algebra Premium
- Power iterationMediumLinear AlgebraProgramming & DSA Premium
- Power of three in a factorialMediumCombinatorics Premium
- Projecting onto a lineMediumLinear Algebra Premium
- Quickselect average complexityMediumProgramming & DSA Premium
- Reading an R²MediumStatistics Premium
- Recovering an eigenvector from its eigenvalueMediumLinear Algebra Premium
- Regression to the meanMediumBrainteasersStatistics Premium
- Renewal-reward fraction of time runningMediumExpected ValueStochastic Processes Premium
- Return time from a three-state chainMediumStochastic Processes Premium
- Right angles in 12 hoursMediumBrainteasers Premium
- Risk-neutral up probabilityMediumStochastic ProcessesFinance & Derivatives Premium
- Screening a rare diseaseMediumConditional Probability & ExpectationStatistics Premium
- Second moment via the MGFMediumRandom VariablesCalculus Premium
- Second-price auction strategyMediumProbabilityMarket Making & Betting Games Premium
- Short-rate modelsMediumStochastic ProcessesFinance & Derivatives Premium
- Singular values via AᵀAMediumLinear Algebra Premium
- Sizing an index-futures hedge in contractsMediumStatisticsFinance & Derivatives Premium
- Spam filterMediumProbabilityConditional Probability & Expectation Premium
- Squares on a chessboardMediumCombinatoricsBrainteasers Premium
- Stationary distribution of a two-state chainMediumProbabilityStochastic Processes Premium
- Subsets with no neighborsMediumCombinatorics Premium
- Sum of squared standard normalsMediumRandom VariablesStatistics Premium
- The cab problemMediumProbabilityConditional Probability & Expectation Premium
- The first component to failMediumRandom Variables Premium
- The painted cubeMediumBrainteasers Premium
- Trace of A-transpose-AMediumLinear Algebra Premium
- Two eggs, one hundred floorsMediumProgramming & DSA Premium
- Two positive testsMediumProbabilityConditional Probability & Expectation Premium
- Variance explained by a regressionMediumStatisticsLinear Algebra Premium
- Variance of a lognormalMediumRandom VariablesFinance & Derivatives Premium
- Variance of a squared normalMediumRandom VariablesStatistics Premium
- Variance of a two-regime returnMediumRandom VariablesStatistics Premium
- Variance-minimizing hedgeMediumProbabilityStatistics Premium
- What 'unbiased' meansMediumStatistics Premium
- Which machine made the defect?MediumConditional Probability & ExpectationStatistics Premium
- Why covariance matrices are PSDMediumStatisticsLinear Algebra Premium
- Winning from deuceMediumProbabilityConditional Probability & Expectation Premium
- k-th order statisticMediumExpected ValueStatistics Premium
- x^4 coefficient of a composed seriesMediumCalculus Premium
- A telescoping partial-fraction sumHardCalculus Premium
- Absorption in naive floating-point summationHardCalculusProgramming & DSA Premium
- Ages from product and sumHardCombinatoricsBrainteasers Premium
- Amoeba extinctionHardProbabilityStochastic Processes Premium
- Bertrand's chordHardProbabilityBrainteasers Premium
- Blue-eyed islandersHardBrainteasers Premium
- Branching process extinction (supercritical)HardProbabilityStochastic Processes Premium
- Broken-stick triangleHardProbability Premium
- Buffon's needleHardProbabilityCalculus Premium
- Correlation of min and maxHardProbabilityRandom Variables Premium
- Cycles in a shuffleHardCombinatoricsExpected Value Premium
- Draws until a smaller valueHardExpected Value Premium
- Ehrenfest urn stationary distributionHardProbabilityStochastic Processes Premium
- Expected duration of a fair walkHardExpected ValueStochastic Processes Premium
- Expected revisits of the start stateHardExpected ValueStochastic Processes Premium
- Exponential martingale compensatorHardCalculusStochastic Processes Premium
- Handshakes at a dinner partyHardCombinatoricsBrainteasers Premium
- Hats with 100 colorsHardBrainteasers Premium
- Inverse via Cayley–HamiltonHardLinear Algebra Premium
- Laplace's rule of successionHardProbabilityConditional Probability & Expectation Premium
- Last one standingHardCombinatoricsBrainteasers Premium
- Making change in lineHardCombinatoricsStochastic Processes Premium
- Median of a streamHardStatisticsProgramming & DSA Premium
- Minimum coins where greedy failsHardProgramming & 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 a scaled Itô integralHardCalculusStochastic Processes Premium
- Reflected paths ending below the levelHardProbabilityStochastic Processes Premium
- Repainting balls to one colorHardExpected ValueStochastic Processes Premium
- Reservoir samplingHardStatisticsProgramming & DSA Premium
- The racing camelsHardBrainteasers Premium
- The two-envelopes paradoxHardProbabilityConditional Probability & Expectation Premium
- Triangle from three independent sticksHardProbabilityCalculus Premium
- Two Newton iterations for a square rootHardCalculusProgramming & DSA Premium
- Two coprime integersHardProbabilityCombinatorics Premium
- Two eggs, 100 floorsHardBrainteasers Premium
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Start practising freeFrequently asked questions
- What does a data-driven research interview focus on?
- Probability and statistics plus data-structures-and-algorithms, with an emphasis on rigorous, model-driven reasoning. Research roles weight statistics; engineering roles weight coding.
- How do I prepare?
- Build deep probability and statistics fluency and, for technical roles, practise algorithms and clean implementation. Reviewing worked solutions reinforces the rigour this format rewards.
- How collaborative are these interviews really?
- Quite. The tone is closer to working a problem together than a quiz, so thinking aloud is an asset and taking an offered hint is not a penalty.