Quant Researcher Interview Questions
Quant researcher interviews go deeper than trading rounds on statistics, distributions and stochastic processes, and add open-ended problems where you reason about data and defend a model.
Expect rigorous probability and statistics: estimators and their properties, distributions and their tails, conditional expectation, regression and inference, and stochastic processes such as random walks, Markov chains and martingales. Derivations matter, and being able to justify a step matters more than recalling a result.
Alongside that, expect open-ended, data-driven problems - often on a provided dataset - plus coding, commonly in Python. The work in these roles ranges from simple statistics through to machine learning, so breadth and first-principles reasoning are both assessed.
725 questions tagged to Quant Researcher · 465 free to practise now.
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Research interviews reward depth and rigour. Target them with:
- A coin that branches into a dieEasyCombinatoricsExpected ValueView →
- A die with one face decrementedEasyProbabilityConditional Probability & ExpectationView →
- A divisor of a power of tenEasyProbabilityCombinatoricsView →
- A factorial ratio that's a factorialEasyBrainteasersView →
- A guest list with a feudEasyCombinatoricsView →
- A limit that hides a difference of logsEasyCalculusView →
- A mile with no windEasyBrainteasersView →
- A mixed second partial derivativeEasyCalculusView →
- A multiple of 15 in ones and zerosEasyBrainteasersView →
- A race between two small-angle ratesEasyCalculusView →
- A ratio of Fibonacci sumsEasyBrainteasersView →
- A root of a product plus oneEasyBrainteasersView →
- A specific sequence given three headsEasyProbabilityConditional Probability & ExpectationView →
- A sum of four before a sum of twoEasyProbabilityView →
- A sum of three cubesEasyBrainteasersView →
- A two-sigma tail probabilityEasyRandom VariablesStatisticsView →
- Age in a square yearEasyBrainteasersView →
- All four aces before any kingEasyProbabilityCombinatoricsView →
- All the squares on a chessboardEasyCombinatoricsBrainteasersView →
- American early exerciseEasyFinance & DerivativesView →
- An alternating sum of squaresEasyBrainteasersView →
- An infinite nested radicalEasyBrainteasersView →
- An odd subset with two small elementsEasyCombinatoricsView →
- Angle under an orthogonal mapEasyLinear AlgebraView →
- Arranging colored balls in a lineEasyCombinatoricsView →
- At least one blue and one greenEasyProbabilityCombinatoricsView →
- Average distance on an intervalEasyRandom VariablesView →
- Backing out the correlation from portfolio riskEasyRandom VariablesStatisticsView →
- Beating a product of uniformsEasyProbabilityRandom VariablesView →
- Beating three othersEasyProbabilityRandom VariablesView →
- Break-even move after a round tripEasyFinance & DerivativesView →
- Chebyshev on a concrete intervalEasyStatisticsView →
- Chi-square test for a varianceEasyStatisticsView →
- Clock angle at 3:15EasyBrainteasersView →
- Coin rolling around a coinEasyBrainteasersView →
- Color switches in a drawEasyRandom VariablesExpected ValueView →
- Correlation from a summed varianceEasyRandom VariablesStatisticsView →
- Correlation of two event indicatorsEasyProbabilityStatisticsView →
- Correlation under rescalingEasyRandom VariablesStatisticsView →
- Counting 8-bit stringsEasyCombinatoricsView →
- Counting complement pairsEasyProgramming & DSAView →
- Counting flushesEasyProbabilityCombinatoricsView →
- Counting nines to 1000EasyCombinatoricsBrainteasersView →
- Counting up-down walks to a targetEasyCombinatoricsView →
- Covariance of a chi-square and a ratioEasyRandom VariablesStatisticsView →
- Covariance of summed Brownian motionsEasyStochastic ProcessesView →
- Crossing the origin twiceEasyStochastic 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 →
- Dots on distinct edgesEasyProbabilityCombinatoricsView →
- Eigenvalues of a 2×2 matrixEasyLinear AlgebraView →
- Even count until the coin repeatsEasyProbabilityView →
- Even heads with one fair coinEasyProbabilityConditional Probability & ExpectationView →
- Even numbers, distinct digitsEasyCombinatoricsView →
- Even-size, non-empty subsetEasyProbabilityCombinatoricsView →
- Exactly one clears two-thirdsEasyProbabilityRandom VariablesView →
- Expected distance of a dart from centerEasyProbabilityRandom VariablesView →
- Expected flips after a losing startEasyProbabilityExpected ValueView →
- Expected flips for three headsEasyProbabilityExpected ValueView →
- Expected flips for two heads in a rowEasyProbabilityExpected ValueView →
- Finding the number of blue socksEasyProbabilityCombinatoricsView →
- First tail within two flipsEasyProbabilityView →
- Four dice summing to twentyEasyProbabilityCombinatoricsView →
- Handshakes at four couplesEasyCombinatoricsBrainteasersView →
- How many sixes on the die?EasyExpected ValueBrainteasersView →
- Integers that contain a zeroEasyCombinatoricsBrainteasersView →
- Interior crossings of a decagon's diagonalsEasyCombinatoricsView →
- Interquartile range of an exponentialEasyRandom VariablesStatisticsView →
- Keep it or draw againEasyProbabilityExpected ValueView →
- Keep the d8 or gamble on the d12?EasyProbabilityExpected ValueView →
- Landing two above the startEasyStochastic ProcessesView →
- Lapping on the trackEasyBrainteasersView →
- Largest eigenvalue after squaringEasyLinear AlgebraView →
- Largest possible covarianceEasyRandom VariablesStatisticsView →
- Lattice paths through a checkpointEasyCombinatoricsView →
- MISSISSIPPI with the P's togetherEasyCombinatoricsView →
- Matching a max and a min at zeroEasyProbabilityView →
- Matching a uniform and an exponentialEasyRandom VariablesStatisticsView →
- Matching locks to keysEasyBrainteasersView →
- Maximum of four uniforms in a bandEasyProbabilityRandom VariablesView →
- More heads than tails in six flipsEasyProbabilityView →
- Multiplications saved by Horner's methodEasyProgramming & DSAView →
- No heads in a random number of flipsEasyProbabilityRandom VariablesView →
- Norm after imposing orthogonalityEasyLinear AlgebraView →
- Normalizing a tilted densityEasyRandom VariablesCalculusView →
- One blue die matches the redEasyProbabilityView →
- Origin between two pointsEasyProbabilityView →
- Paid a dollar or the drawEasyExpected ValueStatisticsView →
- Paid the last roll before you stopEasyProbabilityExpected ValueView →
- Parameter values for a singular matrixEasyLinear AlgebraView →
- Polygons with integer anglesEasyBrainteasersView →
- Pooling two independent estimatesEasyRandom VariablesStatisticsView →
- Posterior from a likelihood ratioEasyConditional Probability & ExpectationStatisticsView →
- Profit from a favourable stopping gameEasyExpected ValueStochastic ProcessesView →
- R-squared from the sums of squaresEasyStatisticsView →
- R-squared when you duplicate every pointEasyStatisticsView →
- Reflipping for valueEasyProbabilityExpected ValueView →
- Regressing with zero covarianceEasyRandom VariablesStatisticsView →
- Retries under a hard capEasyExpected ValueStochastic ProcessesView →
- Ripple on a pondEasyCalculusView →
- Rolling a die to size the next dieEasyConditional Probability & ExpectationExpected ValueView →
- Rolling until you match the first rollEasyProbabilityExpected ValueView →
- Rolls until an even sumEasyProbabilityExpected ValueView →
- Round table with a couple togetherEasyCombinatoricsView →
- Same side four timesEasyProbabilityView →
- Sample SD with Bessel's correctionEasyStatisticsView →
- Second moment from varianceEasyRandom VariablesStatisticsView →
- Sharing your weekday of birthEasyProbabilityView →
- Sharpe of two combined uncorrelated strategiesEasyStatisticsFinance & DerivativesView →
- Shrinking the standard errorEasyStatisticsView →
- Six heads from a random biased coinEasyConditional Probability & ExpectationRandom VariablesView →
- Skewness of a Laplace variableEasyRandom VariablesStatisticsView →
- Slope of a product at a special pointEasyCalculusView →
- Solving a linear Diophantine equationEasyBrainteasersView →
- Spread of a two-card sumEasyRandom VariablesStatisticsView →
- Standard deviation of a correlated sumEasyRandom VariablesStatisticsView →
- Sum of cubed eigenvaluesEasyLinear AlgebraView →
- Sum of the OLS coefficientsEasyStatisticsView →
- Tangent-minus-sine third-order limitEasyCalculusView →
- The added babyEasyProbabilityConditional Probability & ExpectationView →
- The higher die shows a fourEasyProbabilityView →
- The largest unmakeable postageEasyBrainteasersView →
- The peak of a decaying pulseEasyCalculusView →
- The price of a triangular gardenEasyBrainteasersView →
- The top two cards form a pairEasyProbabilityCombinatoricsView →
- The weight of the fishEasyBrainteasersView →
- Three cube faces at a cornerEasyProbabilityCombinatoricsView →
- Three distinct dice, no sixEasyProbabilityCombinatoricsView →
- Three primes in six rollsEasyProbabilityView →
- Three raids on the flockEasyBrainteasersView →
- Three-one strings with matching endpointsEasyCombinatoricsView →
- Timing the revolverEasyBrainteasersView →
- Top three dice summing to eighteenEasyProbabilityCombinatoricsView →
- Two mismatched diceEasyProbabilityView →
- Two numbers in different groupsEasyProbabilityCombinatoricsView →
- Two ordering constraints at onceEasyProbabilityCombinatoricsView →
- Two primes with an even sumEasyProbabilityCombinatoricsView →
- Unchanged after ten swingsEasyProbabilityBrainteasersView →
- Units digit of a random productEasyProbabilityCombinatoricsView →
- Upper bound on a dry weekendEasyProbabilityView →
- Variance of a sum of Brownian motionEasyStochastic ProcessesView →
- Variance of an asymmetric random walkEasyRandom VariablesStochastic ProcessesView →
- Ways to reach deuceEasyProbabilityCombinatoricsView →
- Weighting a fixed sumEasyConditional Probability & ExpectationExpected ValueView →
- When the clock hands next meetEasyBrainteasersView →
- When the colony outgrows its life supportEasyBrainteasersCalculusView →
- Where the arrivals landEasyProbabilityStochastic ProcessesView →
- Where the maximum landsEasyRandom VariablesStatisticsView →
- Where x squared log x bottoms outEasyCalculusView →
- Whether either bus comes soonEasyProbabilityRandom VariablesView →
- Which side holds the heavy weightEasyProbabilityCombinatoricsView →
- Winning by a growing marginEasyProbabilityBrainteasersView →
- 1000 bottles, one poisonedMediumBrainteasersView →
- 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 ladder slipping in oilMediumCalculusView →
- A large power, modular orderMediumProgramming & DSAView →
- A low medianMediumProbabilityRandom VariablesView →
- A point near the cone's baseMediumProbabilityCalculusView →
- A prime sum on prime diceMediumProbabilityCombinatoricsView →
- A ratio of gamma valuesMediumRandom VariablesView →
- A tenth power of a matrixMediumLinear AlgebraView →
- Adults before the busMediumBrainteasersView →
- Age a fraction of the birth yearMediumBrainteasersView →
- All six faces (coupon collector)MediumRandom VariablesExpected ValueView →
- An ace for everyoneMediumProbabilityCombinatoricsView →
- An ace in every pileMediumProbabilityCombinatoricsView →
- An ant returning to its cornerMediumExpected ValueStochastic ProcessesView →
- Anagrams of LOLLIPOPMediumCombinatoricsView →
- Average salary, kept privateMediumBrainteasersStatisticsView →
- Balanced parenthesesMediumCombinatoricsProgramming & DSAView →
- Balancing six- and eight-sided diceMediumExpected ValueBrainteasersView →
- Bayes: did it rain?MediumConditional Probability & ExpectationStatisticsView →
- Bertrand's boxMediumProbabilityConditional Probability & ExpectationView →
- Best linear blend of two estimatesMediumRandom VariablesStatisticsView →
- Boy–girl neighbors in a lineMediumCombinatoricsExpected ValueView →
- Cash out or bustMediumProbabilityExpected ValueView →
- Cats and dogs on the streetMediumBrainteasersView →
- Chords that don't crossMediumProbabilityCombinatoricsView →
- Coin sets the number of dice rollsMediumProbabilityConditional Probability & ExpectationView →
- Coin-pile NimMediumBrainteasersMarket Making & Betting GamesView →
- 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 →
- Cutting a cube into 27MediumBrainteasersView →
- Deleting every other number on a circleMediumCombinatoricsBrainteasersView →
- Density of a sum of two uniformsMediumProbabilityRandom VariablesView →
- Density of a uniform squaredMediumRandom VariablesCalculusView →
- Derivative of xˣMediumCalculusView →
- Dice game, up to three rollsMediumExpected ValueStochastic ProcessesView →
- Dice payoff via WaldMediumExpected ValueStochastic ProcessesView →
- Digits multiplying to half the numberMediumBrainteasersView →
- Digits of concatenated powersMediumBrainteasersView →
- Disease test (Bayes)MediumConditional Probability & ExpectationStatisticsView →
- Distinct die labelingsMediumCombinatoricsBrainteasersView →
- Distinct faces in three rollsMediumExpected ValueView →
- Distributing candies with a capMediumCombinatoricsView →
- E[X | X > 0] for a standard normalMediumStatisticsCalculusView →
- Eigenvalues of a projectionMediumLinear AlgebraView →
- Eigenvalues of a rotationMediumLinear AlgebraView →
- Eight dice summing to twelveMediumProbabilityCombinatoricsView →
- Emptying the cherry bowlMediumProbabilityCombinatoricsView →
- Enlarging a square orchardMediumBrainteasersView →
- Exactly two aces in a bridge handMediumProbabilityCombinatoricsView →
- Expectation as a sum of tailsMediumRandom VariablesExpected ValueView →
- Expected fives before the first sixMediumProbabilityExpected ValueView →
- Expected flips for HHMediumRandom VariablesExpected ValueView →
- Expected flips for HHTMediumExpected ValueStochastic ProcessesView →
- Expected flips for HTMediumExpected ValueStochastic ProcessesView →
- Expected gap between two normalsMediumRandom VariablesView →
- Expected gap on 30-sided diceMediumProbabilityExpected ValueView →
- Expected maximum of two diceMediumRandom VariablesExpected ValueView →
- Expected median of three diceMediumProbabilityExpected ValueView →
- Expected square of a random unit complex numberMediumProbabilityRandom VariablesView →
- Expected value of the highest cardMediumProbabilityExpected ValueView →
- Fair outcome from a biased coinMediumProbabilityStatisticsView →
- First HH on the tenth tossMediumProbabilityCombinatoricsView →
- First consecutive repeatMediumProbabilityExpected ValueView →
- First head on an even flipMediumProbabilityView →
- First head strictly soonerMediumProbabilityRandom VariablesView →
- First passage to ±1MediumStochastic ProcessesView →
- First to three of a kind in a rowMediumProbabilityExpected ValueView →
- Four fives before the first sixMediumProbabilityRandom VariablesView →
- Four points on a semicircleMediumProbabilityView →
- Four times as long to the first headMediumProbabilityRandom VariablesView →
- Full housesMediumProbabilityCombinatoricsView →
- Gambler's ruinMediumProbabilityStochastic ProcessesView →
- Gambler's ruin (unfair)MediumProbabilityStochastic ProcessesView →
- Grandmother's age from the digitsMediumBrainteasersView →
- Growth rate of a rank-one eigenvalueMediumLinear AlgebraView →
- Guess 2/3 of the averageMediumMarket Making & Betting GamesView →
- Heads given the ends differMediumConditional Probability & ExpectationExpected ValueView →
- How fast the bubble's skin growsMediumCalculusView →
- How large can the off-diagonal be?MediumLinear AlgebraView →
- How much a control variate helpsMediumFinance & DerivativesProgramming & DSAView →
- Integrating arctangent by partsMediumCalculusView →
- Is W(t)³ a martingale?MediumStochastic ProcessesView →
- Keeping two apartMediumCombinatoricsView →
- Kelly sizing on an asymmetric betMediumMarket Making & Betting GamesView →
- Largest circle in a triangleMediumBrainteasersView →
- Largest eigenvalue of a rank-one updateMediumLinear AlgebraView →
- Lattice paths in 3DMediumCombinatoricsView →
- Letters into envelopesMediumProbabilityExpected ValueView →
- Log-dynamics of a geometric Brownian motionMediumStochastic ProcessesView →
- Matching floors of a logarithmMediumProbabilityRandom VariablesView →
- Maximize xyz on a planeMediumCalculusView →
- Maximum of x^(1/x)MediumCalculusView →
- Maximum variance on an intervalMediumRandom VariablesStatisticsView →
- Mean over variance of a nested uniformMediumProbabilityRandom VariablesView →
- Median of a list and its squaresMediumCombinatoricsStatisticsView →
- Minimum of two exponentialsMediumProbabilityRandom VariablesView →
- Minimum-variance weightsMediumStatisticsFinance & DerivativesView →
- Monotone paths across a gridMediumCombinatoricsView →
- Monty HallMediumProbabilityConditional Probability & ExpectationView →
- Multiplications in fast exponentiationMediumProgramming & DSAView →
- Newton's division-free reciprocalMediumCalculusView →
- No face card before the two of heartsMediumProbabilityCombinatoricsView →
- No two evens adjacentMediumCombinatoricsView →
- No two neighboring bulbs litMediumProbabilityCombinatoricsView →
- Non-attacking rooksMediumCombinatoricsView →
- Norm of a doubly-stochastic stationary vectorMediumLinear AlgebraStochastic ProcessesView →
- Number of runsMediumExpected ValueView →
- OLS slope from four pointsMediumStatisticsView →
- Odd multiples of threeMediumCombinatoricsBrainteasersView →
- Odd solutions to a sumMediumCombinatoricsView →
- One card each in casino warMediumProbabilityCombinatoricsView →
- One extra roll for more primesMediumProbabilityView →
- One hundred animals for a thousand dollarsMediumBrainteasersView →
- One hundred light bulbsMediumBrainteasersView →
- One random subset inside anotherMediumProbabilityCombinatoricsView →
- Order statistics of two uniformsMediumRandom VariablesStatisticsView →
- Placing operators among digitsMediumCombinatoricsView →
- Position of the first aceMediumConditional Probability & ExpectationExpected ValueView →
- Pricing a digital from a call spreadMediumFinance & DerivativesView →
- Probability of three of a kindMediumProbabilityCombinatoricsView →
- Product of two uniforms above a halfMediumProbabilityRandom VariablesView →
- Put–call parity with a dividendMediumFinance & DerivativesView →
- Rank and nullity of a rotationMediumLinear AlgebraView →
- Rate of a growing shadowMediumCalculusView →
- Ratio of partial sumsMediumRandom VariablesExpected ValueView →
- Rebuilding a tower of ten ringsMediumBrainteasersProgramming & DSAView →
- Red faces on a diced cubeMediumCombinatoricsExpected ValueView →
- Regions from ten linesMediumCombinatoricsBrainteasersView →
- Rehedging a book after a moveMediumFinance & DerivativesView →
- Resonance in undetermined coefficientsMediumCalculusView →
- Rolling a 5-sided die to reach fiveMediumProbabilityExpected ValueView →
- Rolling until two rolls differ by twoMediumProbabilityExpected ValueView →
- Rolls to a six before a fiveMediumProbabilityExpected ValueView →
- Russian roulette, re-spunMediumProbabilityConditional Probability & ExpectationView →
- Sampling an exponential from a uniformMediumRandom VariablesProgramming & DSAView →
- Sharpe ratio in a marble gameMediumExpected ValueStatisticsView →
- Simulate probability pMediumProbabilityProgramming & DSAView →
- Smallest simulable probabilityMediumProbabilityBrainteasersView →
- Spectrum of a constant-diagonal matrixMediumLinear AlgebraView →
- Spectrum of a symmetric matrixMediumStatisticsLinear AlgebraView →
- Sum and difference of perfectly correlated variablesMediumRandom VariablesStatisticsView →
- Sum of independent PoissonsMediumProbabilityRandom VariablesView →
- Sum of multinomial coefficientsMediumCombinatoricsView →
- Sum of the pandigital numbersMediumCombinatoricsBrainteasersView →
- Sum versus twice the differenceMediumProbabilityRandom VariablesView →
- Summing digits to a millionMediumCombinatoricsBrainteasersView →
- Swapping the regression variablesMediumStatisticsView →
- Ten dice, sum divisible by sixMediumProbabilityCombinatoricsView →
- Terms in a multinomial expansionMediumCombinatoricsView →
- The Gaussian integralMediumCalculusView →
- The German tank problemMediumExpected ValueStatisticsView →
- The SDE of the reciprocalMediumStochastic ProcessesView →
- The birthday problemMediumProbabilityCombinatoricsView →
- The die that makes sums uniformMediumProbabilityCombinatoricsView →
- The largest unmakeable totalMediumCombinatoricsBrainteasersView →
- The last lightbulb to burn outMediumRandom VariablesExpected ValueView →
- The most balanced factorizationMediumBrainteasersView →
- The same number of tailsMediumProbabilityCombinatoricsView →
- The third shiny pennyMediumProbabilityCombinatoricsView →
- The two-headed coinMediumProbabilityConditional Probability & ExpectationView →
- Three dots on a squareMediumProbabilityCombinatoricsView →
- Three ones in a rowMediumProbabilityCombinatoricsView →
- Three prisonersMediumProbabilityConditional Probability & ExpectationView →
- Three rolls, keep the lastMediumExpected ValueView →
- Three-four-five in Pascal's triangleMediumCombinatoricsBrainteasersView →
- Tiling a stripMediumCombinatoricsView →
- Trace of a productMediumLinear AlgebraView →
- Trailing zeros of 100!MediumCombinatoricsView →
- Tuning an exponential random walkMediumProbabilityStochastic ProcessesView →
- Two childrenMediumProbabilityConditional Probability & ExpectationView →
- Two guards, two doorsMediumBrainteasersView →
- Two ropes, 45 minutesMediumBrainteasersView →
- Uncorrelated but dependentMediumRandom VariablesStatisticsView →
- Units digit of a random powerMediumProbabilityCombinatoricsView →
- Value of iⁱMediumCalculusView →
- Variance of a Brownian combinationMediumStochastic ProcessesView →
- Variance of a coin-gated payoffMediumRandom VariablesStatisticsView →
- 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 →
- Variance of the longer pieceMediumProbabilityRandom VariablesView →
- Volume where two cylinders crossMediumCalculusView →
- Waiting to see both facesMediumRandom VariablesStatisticsView →
- When the naive shuffle is biasedMediumProgramming & DSAView →
- Which deck for two reds?MediumProbabilityView →
- Whose draw is larger?MediumProbabilityView →
- Why divide by n−1?MediumStatisticsView →
- Will they meet?MediumProbabilityView →
- X positive given the sum is positiveMediumProbabilityRandom VariablesView →
- A 12 before two 7sHardProbabilityStochastic ProcessesView →
- A Fibonacci power sumHardBrainteasersView →
- A coin thick enough to land on its sideHardProbabilityBrainteasersView →
- A flea's shortest escape across a boxHardBrainteasersCalculusView →
- 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 second red ball from the same urnHardProbabilityConditional Probability & ExpectationView →
- A small sub-triangleHardProbabilityRandom VariablesView →
- A three-way race to the first headHardProbabilityRandom VariablesView →
- A triangle of consecutive integersHardBrainteasersView →
- A weighted sum of binomialsHardCombinatoricsBrainteasersView →
- Average of near-diagonal numbersHardCombinatoricsBrainteasersView →
- Balls into bowls, three eachHardCombinatoricsView →
- Cars advancing to the endHardProbabilityExpected ValueView →
- Cats and miceHardBrainteasersView →
- Conditioning a Brownian bridgeHardStochastic ProcessesView →
- Counting fives before a four and a sixHardProbabilityRandom VariablesView →
- Covariance of X with Y squaredHardRandom VariablesStatisticsView →
- Covariance with a lognormal childHardConditional Probability & ExpectationRandom VariablesView →
- Cubes over the terminating denominatorsHardBrainteasersCalculusView →
- Cuts until one orb remainsHardProbabilityExpected ValueView →
- Dealing until kings or a king-and-aceHardCombinatoricsExpected ValueView →
- Digits with distinct pairwise sumsHardCombinatoricsBrainteasersView →
- Distinct toys from seven boxesHardProbabilityExpected ValueView →
- Domino tilings of a 3×8 gridHardCombinatoricsView →
- Doors toggled by primesHardCombinatoricsBrainteasersView →
- Draws to beat a hidden uniformHardRandom VariablesExpected ValueView →
- Draws to pass a log thresholdHardProbabilityRandom VariablesView →
- Draws to pass twoHardProbabilityRandom VariablesView →
- Everyone gets one of eachHardProbabilityCombinatoricsView →
- Expected arc covering a fixed pointHardProbabilityExpected ValueView →
- Expected chord between two random pointsHardProbabilityExpected ValueView →
- Expected chord intersectionsHardProbabilityCombinatoricsView →
- Expected largest of ten ballsHardCombinatoricsExpected ValueView →
- Expected local maxima in a shuffleHardProbabilityExpected ValueView →
- Filling three bins from a coin flipHardProbabilityCombinatoricsView →
- Guessing cards from a known pileHardProbabilityExpected ValueView →
- HTH before HHTHardProbabilityRandom VariablesView →
- Head density with no two in a rowHardProbabilityCombinatoricsView →
- Hitting zero on a ringHardProbabilityStochastic ProcessesView →
- How many long cycles?HardProbabilityCombinatoricsView →
- Laplace transform of a Brownian exit timeHardStochastic ProcessesView →
- Largest pairwise-coprime subset sumHardCombinatoricsBrainteasersView →
- Locks for a four-of-seven safeHardCombinatoricsBrainteasersView →
- Long cycles in a random permutationHardCombinatoricsExpected ValueView →
- Loops from tying noodlesHardProbabilityExpected ValueView →
- Making a power of Brownian motion a martingaleHardStochastic ProcessesView →
- Mean of a mean-reverting processHardStochastic ProcessesFinance & DerivativesView →
- Measuring two pintsHardBrainteasersView →
- More coins, more heads?HardProbabilityCombinatoricsView →
- No two samples too closeHardProbabilityCombinatoricsView →
- Odd sums on a 3×3 gridHardProbabilityCombinatoricsView →
- One of each face before the two of heartsHardProbabilityCombinatoricsView →
- Only seven left unchosenHardProbabilityCombinatoricsView →
- Overshoot past oneHardProbabilityRandom VariablesView →
- Pairing gloves within oneHardProbabilityCombinatoricsView →
- Pairing with a difference of 1 or 11HardCombinatoricsBrainteasersView →
- Pairs left in the drawerHardCombinatoricsExpected ValueView →
- Penalty kicks with a shifting rateHardProbabilityRandom VariablesView →
- Pirate gameHardMarket Making & Betting GamesView →
- Quadratic variation in mean-squareHardStochastic ProcessesView →
- Range beats the midpointHardProbabilityRandom VariablesView →
- Reading N(d₂) in Black–ScholesHardFinance & DerivativesView →
- Rolling until two rolls are closeHardProbabilityExpected ValueView →
- Rolls to a six, given all evenHardConditional Probability & ExpectationExpected ValueView →
- Rotations divisible by 37HardCombinatoricsBrainteasersView →
- Rounds to see all faces with two diceHardProbabilityExpected ValueView →
- Runs of red and blue marblesHardCombinatoricsExpected ValueView →
- Second moment of a Gaussian-kernel stochastic integralHardCalculusStochastic ProcessesView →
- Seven seated in age orderHardProbabilityCombinatoricsView →
- Shortest of three piecesHardProbabilityRandom VariablesView →
- Shuffles to restore the deckHardCombinatoricsBrainteasersView →
- Six pieces, none past a halfHardProbabilityRandom VariablesView →
- Smallest card sharing a boxHardProbabilityExpected ValueView →
- Smallest number with digit product 10000HardCombinatoricsBrainteasersView →
- 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 →
- Sums of fours and fivesHardCombinatoricsBrainteasersView →
- Ten prime digits with a set productHardCombinatoricsView →
- The boy born on a TuesdayHardProbabilityConditional Probability & ExpectationView →
- The decreasing run of uniformsHardRandom VariablesExpected ValueView →
- The drunk passengerHardProbabilityConditional Probability & ExpectationView →
- The frog's single leftward hopHardProbabilityCombinatoricsView →
- The leap-frog's favorite landing spotHardProbabilityStochastic ProcessesView →
- The number with no new digitsHardBrainteasersView →
- The reroll advantage in a die duelHardProbabilityMarket Making & Betting GamesView →
- The snow plowHardCalculusView →
- The survivor in the circleHardBrainteasersView →
- Three eggs, nine dropsHardCombinatoricsBrainteasersView →
- Three first-heads in non-decreasing orderHardProbabilityRandom VariablesView →
- Triangle with equal side sumsHardCombinatoricsBrainteasersView →
- Twelve balls, one oddHardBrainteasersView →
- Two Brownian values, both positiveHardProbabilityStochastic ProcessesView →
- Two random segments overlappingHardProbabilityRandom VariablesView →
- Two random subsets that overlapHardProbabilityCombinatoricsView →
- 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 →
- Weighings for the odd beanHardBrainteasersView →
- When a power of the process is a submartingaleHardProbabilityStochastic ProcessesView →
- When a uniform ratio rounds to a squareHardProbabilityRandom VariablesView →
- When k-to-the-k is a squareHardCombinatoricsBrainteasersView →
- When the extremes sum above oneHardProbabilityRandom VariablesView →
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Start practising freeFrequently asked questions
- How are quant researcher interviews different from trader interviews?
- They go substantially deeper on statistics and probability theory and expect you to derive results rather than recall them. Trading rounds prize speed and decisiveness; research rounds prize rigour, and give you more time to show it.
- Which topics matter most for a quant research interview?
- Probability and statistics first - distributions, estimators, conditional expectation and inference - then stochastic processes, linear algebra and coding. Machine learning appears for some teams but rarely replaces the fundamentals.
- How much coding is involved?
- Enough to matter. Python is the usual language, and you should be comfortable implementing a simulation or a numerical routine cleanly, even if the role is not primarily an engineering one.