Random Variables Interview Questions for Quant Researchers
Quant Researchers get asked random variables differently from other quant roles - the emphasis shifts with what the job actually does. This is that slice.
127 questions, all free to practise. The split is 28 easy, 69 medium, 30 hard.
- A two-sigma tail probabilityEasyRandom VariablesStatisticsView →
- Average distance on an intervalEasyRandom VariablesView →
- Backing out the correlation from portfolio riskEasyRandom VariablesStatisticsView →
- Beating a product of uniformsEasyProbabilityRandom VariablesView →
- Beating three othersEasyProbabilityRandom VariablesView →
- Color switches in a drawEasyRandom VariablesExpected ValueView →
- Correlation from a summed varianceEasyRandom VariablesStatisticsView →
- Correlation under rescalingEasyRandom VariablesStatisticsView →
- Covariance of a chi-square and a ratioEasyRandom VariablesStatisticsView →
- Exactly one clears two-thirdsEasyProbabilityRandom VariablesView →
- Expected distance of a dart from centerEasyProbabilityRandom VariablesView →
- Interquartile range of an exponentialEasyRandom VariablesStatisticsView →
- Largest possible covarianceEasyRandom VariablesStatisticsView →
- Matching a uniform and an exponentialEasyRandom VariablesStatisticsView →
- Maximum of four uniforms in a bandEasyProbabilityRandom VariablesView →
- No heads in a random number of flipsEasyProbabilityRandom VariablesView →
- Normalizing a tilted densityEasyRandom VariablesCalculusView →
- Pooling two independent estimatesEasyRandom VariablesStatisticsView →
- Regressing with zero covarianceEasyRandom VariablesStatisticsView →
- Second moment from varianceEasyRandom VariablesStatisticsView →
- Six heads from a random biased coinEasyConditional Probability & ExpectationRandom VariablesView →
- Skewness of a Laplace variableEasyRandom VariablesStatisticsView →
- Spread of a two-card sumEasyRandom VariablesStatisticsView →
- Standard deviation of a correlated sumEasyRandom VariablesStatisticsView →
- Two searches, neither hitsEasyRandom VariablesView →
- Variance of an asymmetric random walkEasyRandom VariablesStochastic ProcessesView →
- Where the maximum landsEasyRandom VariablesStatisticsView →
- Whether either bus comes soonEasyProbabilityRandom VariablesView →
- A convexity gap by JensenMediumRandom VariablesExpected ValueView →
- A difference of three normalsMediumRandom VariablesStatisticsView →
- A divergent reciprocal expectationMediumRandom VariablesCalculusView →
- A low medianMediumProbabilityRandom VariablesView →
- A ratio of gamma valuesMediumRandom VariablesView →
- All six faces (coupon collector)MediumRandom VariablesExpected ValueView →
- At least two sixes in five rollsMediumProbabilityRandom VariablesView →
- Backing out a correlationMediumRandom VariablesStatisticsView →
- Best linear blend of two estimatesMediumRandom VariablesStatisticsView →
- Conditional mean on a circleMediumConditional Probability & ExpectationRandom VariablesView →
- Correlation of overlapping sumsMediumRandom VariablesStatisticsView →
- Covariance from a triangular densityMediumRandom VariablesStatisticsView →
- Covariance of sum and differenceMediumRandom VariablesStatisticsView →
- Density of a sum of two uniformsMediumProbabilityRandom VariablesView →
- Density of a uniform squaredMediumRandom VariablesCalculusView →
- Expectation as a sum of tailsMediumRandom VariablesExpected ValueView →
- Expectation of e raised to a normalMediumRandom VariablesExpected ValueView →
- Expectation of −2 ln UMediumRandom VariablesCalculusView →
- Expected flips for HHMediumRandom VariablesExpected ValueView →
- Expected gap between two normalsMediumRandom VariablesView →
- Expected maximum of three diceMediumRandom VariablesExpected ValueView →
- Expected maximum of two diceMediumRandom VariablesExpected ValueView →
- Expected minimum of two diceMediumRandom VariablesExpected ValueView →
- Expected square of a random unit complex numberMediumProbabilityRandom VariablesView →
- First head strictly soonerMediumProbabilityRandom VariablesView →
- Four fives before the first sixMediumProbabilityRandom VariablesView →
- Four times as long to the first headMediumProbabilityRandom VariablesView →
- Fourth moment of a shifted normalMediumProbabilityRandom VariablesView →
- How many trials to poll a proportionMediumRandom VariablesStatisticsView →
- Matching floors of a logarithmMediumProbabilityRandom VariablesView →
- Maximum variance on an intervalMediumRandom VariablesStatisticsView →
- Mean over variance of a nested uniformMediumProbabilityRandom VariablesView →
- Median of a linear densityMediumRandom VariablesCalculusView →
- Memoryless waitingMediumConditional Probability & ExpectationRandom VariablesView →
- Minimum of two exponentialsMediumProbabilityRandom VariablesView →
- Neither die exceeds fourMediumProbabilityRandom VariablesView →
- Optimally pooling two estimatorsMediumRandom VariablesStatisticsView →
- Order statistics of two uniformsMediumRandom VariablesStatisticsView →
- Poisson thinning: exactly two large ordersMediumRandom VariablesView →
- Product of two uniforms above a halfMediumProbabilityRandom VariablesView →
- Rare-event Poisson approximationMediumProbabilityRandom VariablesView →
- Ratio of partial sumsMediumRandom VariablesExpected ValueView →
- Remaining life of a memoryless partMediumRandom VariablesView →
- Sampling an exponential from a uniformMediumRandom VariablesProgramming & DSAView →
- Second moment via the MGFMediumRandom VariablesCalculusView →
- Sum and difference of perfectly correlated variablesMediumRandom VariablesStatisticsView →
- Sum of independent PoissonsMediumProbabilityRandom VariablesView →
- Sum of squared standard normalsMediumRandom VariablesStatisticsView →
- Sum versus twice the differenceMediumProbabilityRandom VariablesView →
- The first component to failMediumRandom VariablesView →
- The larger die shows a 4 - what about the smaller?MediumProbabilityRandom VariablesView →
- The last lightbulb to burn outMediumRandom VariablesExpected ValueView →
- The probability integral transformMediumRandom VariablesStatisticsView →
- Two uniforms summing below a halfMediumProbabilityRandom VariablesView →
- Uncorrelated but dependentMediumRandom VariablesStatisticsView →
- Variance of a coin-gated payoffMediumRandom VariablesStatisticsView →
- Variance of a compound daily totalMediumRandom VariablesView →
- Variance of a lognormalMediumRandom VariablesFinance & DerivativesView →
- Variance of a squared normalMediumRandom VariablesStatisticsView →
- Variance of a sum drawn without replacementMediumRandom VariablesView →
- Variance of a two-regime returnMediumRandom VariablesStatisticsView →
- Variance of an aggregate Poisson totalMediumRandom VariablesStochastic ProcessesView →
- Variance of coins-per-die headsMediumRandom VariablesStatisticsView →
- Variance of the larger of two diceMediumRandom VariablesStatisticsView →
- Variance of the longer pieceMediumProbabilityRandom VariablesView →
- Waiting to see both facesMediumRandom VariablesStatisticsView →
- When a biased estimator winsMediumRandom VariablesStatisticsView →
- Which desk books the larger dayMediumRandom VariablesStatisticsView →
- X positive given the sum is positiveMediumProbabilityRandom VariablesView →
- A half-plane, given positiveHardProbabilityRandom VariablesView →
- A small sub-triangleHardProbabilityRandom VariablesView →
- A three-way race to the first headHardProbabilityRandom VariablesView →
- Best-of-seven underdogHardProbabilityRandom VariablesView →
- Correlation of min and maxHardProbabilityRandom VariablesView →
- Counting fives before a four and a sixHardProbabilityRandom VariablesView →
- Covariance of X with Y squaredHardRandom VariablesStatisticsView →
- Covariance with a lognormal childHardConditional Probability & ExpectationRandom VariablesView →
- Draws to beat a hidden uniformHardRandom VariablesExpected ValueView →
- Draws to pass a log thresholdHardProbabilityRandom VariablesView →
- Draws to pass twoHardProbabilityRandom VariablesView →
- HTH before HHTHardProbabilityRandom VariablesView →
- Order statistics are BetaHardRandom VariablesStatisticsView →
- Overshoot past oneHardProbabilityRandom VariablesView →
- Penalty kicks with a shifting rateHardProbabilityRandom VariablesView →
- Range beats the midpointHardProbabilityRandom VariablesView →
- Ratio of two normalsHardRandom VariablesStatisticsView →
- Shortest of three piecesHardProbabilityRandom VariablesView →
- Six pieces, none past a halfHardProbabilityRandom VariablesView →
- Smallest possible MGF valueHardRandom VariablesStatisticsView →
- Spread of a lognormal raised to the fourthHardRandom VariablesStatisticsView →
- Spread of a multinomial count gapHardRandom VariablesStatisticsView →
- The decreasing run of uniformsHardRandom VariablesExpected ValueView →
- Three first-heads in non-decreasing orderHardProbabilityRandom VariablesView →
- Two random segments overlappingHardProbabilityRandom VariablesView →
- Uniforms summing past 1HardRandom VariablesExpected ValueView →
- Variance of the exponential of a gammaHardRandom VariablesStatisticsView →
- Variance under random parametersHardRandom VariablesStatisticsView →
- When a uniform ratio rounds to a squareHardProbabilityRandom VariablesView →
- When the extremes sum above oneHardProbabilityRandom VariablesView →
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