Statistics & Math Interview Questions

Showing 151–180 of 439 results

• GoogleMedium·Data Scientist
  Generate Uniform Samples and Estimate Percentiles

  This problem tests the ability to generate uniform spatial samples using standard random functions and the mathematical application of linear interpolation for percentile estimation from binned data.

  Statistics & MathTechnical ScreenProbabilityStatisticsInterpolation
• GoogleMedium·Machine Learning Engineer
  Generate values by weighted probabilities

  This question evaluates understanding of probabilistic sampling, numerical stability, input validation, and algorithmic trade-offs for streaming weighted random draws, including generator determinism via seeding and methods such as CDF/binary-search versus alias for performance.

  Statistics & MathOnsite
• GoogleMedium·Data Scientist
  Infer distribution and choose robust statistics

  This problem tests the ability to diagnose non-normal data distributions (specifically zero-inflated, heavy-tailed data) and select appropriate statistical metrics for hypothesis testing.

  Statistics & MathTechnical ScreenStatisticsData DistributionsHypothesis Testing
• GoogleMedium·Data Scientist
  Interpreting a Dosage-Recovery Regression: P-values, CIs, Causality

  Given a fitted dosage-vs-recovery-time regression, explain exactly what the reported p-value and confidence interval mean, what assumptions back that inference, how a confidence interval differs from a prediction interval, and why the result alone cannot establish causality. Tests statistical precision under pressure.

  Statistics & MathOnsitestatisticslinear-regressionhypothesis-testing
• GoogleMedium·Data Scientist
  Measure Bird Species Segregation

  This question evaluates spatial statistical reasoning, ecological data analysis, and the ability to formulate hypotheses, choose appropriate segregation metrics, and account for confounders and sampling bias.

  Statistics & MathTechnical Screen
• GoogleMedium·Data Scientist
  Narrow a confidence interval for a mean

  This question evaluates understanding of confidence intervals, the relationship between sample size and interval width, variance-reduction techniques, the impact of changing confidence levels, and the ability to communicate statistical risk and design-based trade-offs.

  Statistics & MathTechnical Screen
• GoogleMedium·Data Scientist
  Prove OLS invariance to linear transforms

  This question evaluates understanding of linear regression invariance under invertible linear transformations, multivariate linear algebra, and the impact of regularization (ridge and lasso) on coefficient and prediction stability in the Statistics & Math domain.

  Statistics & MathTechnical Screen
• GoogleMedium·Data Scientist
  Reading a Regression Slope: P-values, Intervals, and Causality

  Use a fitted slope from a one-predictor regression to explain precisely what a p-value and a confidence interval mean, what assumptions they rest on, how confidence and prediction intervals differ, and why significance is not causation. Tests statistical precision under interview pressure.

  Statistics & MathOnsitestatisticslinear-regressionhypothesis-testing
• GoogleMedium·Data Scientist
  Test a coefficient and explain t-distribution

  This question evaluates a candidate's competence in statistical inference for linear regression—specifically hypothesis testing for OLS coefficients, construction of t-statistics, estimation of standard errors, and the role of estimated error variance—within the Statistics & Math domain for Data Scientist roles.

  Statistics & MathTechnical Screen
• GoogleMedium·Data Scientist
  Test if one value comes from N(μ,σ²)

  This question tests the ability to perform statistical hypothesis testing on a single observation, evaluate the limitations of small sample sizes, and explain the trade-offs between Type I and Type II errors.

  Statistics & MathTechnical ScreenStatisticsHypothesis TestingNormal Distribution
• GoogleMedium·Data Scientist
  Understand Simpson's Paradox with Simple Examples

  This interview question evaluates statistical assumptions, formulas, estimation strategy, uncertainty, edge cases, and interpretation in a realistic interview setting. A strong answer for Understand Simpson's Paradox with Simple Examples states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

  Statistics & MathOnsite
• GustoMedium·Data Scientist
  Compute Parking Clustering Probability and P-Value

  This question tests your ability to calculate exact combinatorial probabilities under a null hypothesis and define a p-value for a spatial clustering test.

  Statistics & MathTechnical ScreenProbabilityCombinatoricsHypothesis Testing
• HHeadlandsMedium·Data Scientist
  Compare Candy-Color Guessing Experiments with Different Sample Sizes

  Evaluate and compare evidence from two binomial experiments with different sample sizes and hit rates against a random guessing null hypothesis.

  Statistics & MathTechnical Screenstatisticshypothesis-testingbinomial-distribution
• HHeadlandsMedium·Data Scientist
  t-Stat With an Added Orthogonal Regressor, Live Sharpe Check, and Absolute-Loss Estimator

  Solve three core quantitative problems covering OLS regression mechanics under orthogonal regressors, statistical significance of backtested Sharpe ratios in live deployment, and loss-function minimization for L1 error.

  Statistics & MathOnline AssessmentEconometricsSharpe RatioLinear Regression
• Hudson River TradingMedium·Software Engineer
  Choose Mean or Median for Trading Profit Metrics

  This problem tests your understanding of statistical measures of central tendency, specifically how different distributions affect the choice between mean and median in high-frequency trading scenarios.

  Statistics & MathTechnical ScreenStatisticsFinanceData Analysis
• Hudson River TradingMedium·Data Scientist
  Compare Mean and Median for a Distribution with a Point Mass

  This question tests the theoretical and empirical comparison between the sample mean and sample median on a mixture distribution containing a discrete point mass and a Gaussian component.

  Statistics & MathTechnical Screenstatisticsprobabilityestimation
• IBMEasy·Data Scientist
  How do you detect and fix multicollinearity?

  This question evaluates understanding of multicollinearity and related competencies in regression diagnostics, feature engineering, model interpretability, and the trade-offs between coefficient inference and predictive performance.

  Statistics & MathTechnical Screen
• ImcHard·Quantitative Trader
  Analyze Optimal Funding Allocations Across Election Districts

  Analyze election-district funding games with weak-composition counting, favorable alignments, explicit allocations, and lower-bound proofs for possible and impossible wins under fixed budgets.

  Statistics & MathTechnical Screen
• InstacartHard·Data Scientist
  Choose tests under non‑normal, unequal variance

  This question tests the ability to select and justify statistical inference methods for metrics that violate standard parametric assumptions, specifically when dealing with heavy-tailed, heteroskedastic, and zero-inflated distributions.

  Statistics & MathOnsiteStatisticsA/B TestingInference
• IEIntercontinental ExchangeMedium·Data Scientist
  Analyze Newton-Raphson Convergence, Choose Sigma, and Derive Vega

  This question evaluates numerical root-finding and option pricing competencies, specifically understanding Newton–Raphson convergence properties, implied volatility inference under the Black–Scholes model, and option sensitivity (Vega).

  Statistics & MathTechnical Screen
• J.P. MorganMedium·Data Scientist
  Interpret Model Metrics, Regularization, and Resampling Fundamentals

  This problem tests your understanding of foundational machine learning metrics for imbalanced classification and the theoretical utility of regularization and resampling techniques.

  Statistics & MathHR ScreenStatisticsMachine LearningRegularization
• JGJain GlobalEasy·Data Scientist
  Define the p-Value, Then Explain How to Test Two Price Series for Cointegration

  Two statistics questions from a systematic trading screen: give a precise definition of the p-value and its common misreadings, then explain what cointegration is and how to test two price series for it. It tests hypothesis-testing rigor, stationarity, the difference between correlation and cointegration, and multiple-testing pitfalls.

  Statistics & MathTechnical Screen
• Jane StreetMedium·Software Engineer
  Calculate win chance in three-player dice game

  This question evaluates understanding of probability theory, conditional probability, and modelling of repeated stochastic events such as ties and rerolls, and is categorized under Statistics & Math.

  Statistics & MathHR Screen
• Jane StreetMedium·Quantitative Trader
  Estimate the Number of Florists in Sydney and Make a Market

  Tests Fermi estimation, sanity checking via dual perspectives (demand vs. supply/geographic), quoting a two-sided market under uncertainty, and updating beliefs given market flow or new information.

  Statistics & MathTechnical ScreenFermi EstimationMarket MakingProbability
• Jane StreetHard·Software Engineer
  Optimal Stopping with Square-Number Ruin

  Analyze an optimal stopping game where a player rolls a fair six-sided die to accumulate points but busts if the running sum hits a positive perfect square. Tests dynamic programming, renewal theory intuition, and rigorous edge-case analysis under uncertain stopping boundaries.

  Statistics & MathTechnical Screenprobabilityoptimal-stoppingdynamic-programming
• Jane StreetHard·Software Engineer
  Optimize a Two-Box Place-or-Take Game

  Analyze and optimize a 100-turn, two-box stochastic game with capacity constraints and opaque states. Derive the optimal decision policy, examine boundary/edge cases, and evaluate how the strategy changes when core assumptions are relaxed.

  Statistics & MathTechnical ScreenProbabilityDynamic ProgrammingMarkov Decision Process
• Jane StreetEasy·Quantitative Trader
  Solve probability and game-theory puzzles

  This set of puzzles evaluates probabilistic reasoning, Bayesian inference, expected-value optimization, optimal stopping, and strategic game-theoretic reasoning under uncertainty and asymmetric information, situated in the Statistics & Math domain.

  Statistics & MathTechnical Screen
• JJefferiesEasy·Data Scientist
  How to compute correlation from variances

  Practice deriving correlation from variance identities for two random variables. The solution explains why Var(X+Y) and Var(X) alone are insufficient, derives covariance and correlation when Var(Y) is known, simplifies the equal-variance case, and checks edge cases where correlation is invalid or inconsistent.

  Statistics & MathTechnical Screen
• JJefferiesMedium·Data Scientist
  How to derive correlation from variances

  Evaluates derivation of correlation from variance identities for two random variables. Strong answers explain why Var(X+Y) and Var(X) alone do not identify correlation, then derive covariance and correlation when Var(Y) is also known.

  Statistics & MathTechnical Screen
• JTJump TradingEasy·Software Engineer
  Find the Largest Equivalence Class of Fractions

  This problem tests your ability to handle numerical equivalence using canonical representations to avoid floating-point precision issues.

  Statistics & MathTechnical ScreenMathHash MapNumber Theory