Statistics & Math Interview Questions

Showing 61–90 of 439 results

• Capital OneEasy·Data Scientist
  Find minimal a for PSD of 3x3 matrix

  This question evaluates understanding of linear algebra concepts such as eigenvalues, matrix definiteness, and spectral properties by asking for the minimal real parameter a that makes a symmetric 3×3 matrix with ones on the diagonal and constant off-diagonal entries positive semidefinite.

  Statistics & MathTechnical Screen
• Capital OneEasy·Data Scientist
  Graph WTP vs content and explain cap

  This question evaluates understanding of piecewise linear functions, marginal analysis, and the economic interpretation of willingness-to-pay, within the Statistics & Math domain for a Data Scientist role.

  Statistics & MathHR Screen
• Capital OneEasy·Data Scientist
  How do you compute expected return for two projects?

  This question tests your ability to calculate the Expected Monetary Value (EMV) of probabilistic outcomes and apply discounting principles to evaluate competing capital investment projects.

  Statistics & MathTechnical ScreenStatisticsFinanceProbability
• Capital OneMedium·Data Scientist
  How to Analyze and Reduce Airline Flight Delays

  This interview question evaluates statistical assumptions, formulas, estimation strategy, uncertainty, edge cases, and interpretation in a realistic interview setting. A strong answer for How to Analyze and Reduce Airline Flight Delays states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

  Statistics & MathTechnical Screen
• Capital OneMedium·Data Scientist
  Interpret regression metrics and assumptions

  This question evaluates a candidate's mastery of multiple linear regression diagnostics and interpretation, covering standardized coefficient interpretation and significance, R²/adjusted R² and out‑of‑fold RMSE comparisons, multicollinearity detection and its effect on coefficients and SEs, heteroskedasticity diagnostics and robust remedies, and implications of intercept omission and partial standardization. Commonly asked in data scientist interviews within the Statistics & Math domain because it probes both conceptual understanding of statistical inference and practical application of model diagnostics and adjustments for reliable prediction and inference.

  Statistics & MathOnsite
• Capital OneMedium·Data Scientist
  Maintain profit margin with new product line

  This question evaluates competence in cost-volume-profit analysis, algebraic modeling of profit margins, and unit economics when adding a new product line.

  Statistics & MathTechnical Screen
• Capital OneEasy·Data Scientist
  Match prior-year profit with new fixed costs

  This question tests the ability to model financial profitability by balancing fixed cost increases against variable profit contributions to maintain a target net income.

  Statistics & MathTechnical ScreenAlgebraFinancial ModelingCVP Analysis
• Capital OneMedium·Data Scientist
  Model network-service unit economics and breakeven

  This question evaluates a data scientist's ability to model unit economics, calculate per-customer contribution and breakeven, and conduct sensitivity and probabilistic churn analysis.

  Statistics & MathOnsite
• Capital OneMedium·Data Scientist
  Optimize profitability for coding contract decisions

  This question evaluates competency in quantitative cost modeling, scheduling, and probabilistic sensitivity analysis within the statistics & math domain, focusing on profit optimization and resource-allocation decisions relevant to a data scientist role.

  Statistics & MathTechnical Screen
• Capital OneMedium·Data Scientist
  Quantify and Model Flight Delays Using Statistical Tests

  Evaluates flight-delay quantification, modeling, and mitigation testing using historical operational data. Strong answers define delay metrics, model delay probability and severity, avoid leakage, and design valid experiments.

  Statistics & MathOnsite
• Capital OneMedium·Data Scientist
  Quantify database bug cost/benefit

  This question evaluates a candidate's ability to perform cohort-based financial impact analysis and basic statistical arithmetic to quantify revenue and cost deltas caused by registration-state errors.

  Statistics & MathTechnical Screen
• Capital OneMedium·Data Scientist
  Set membership fee under investment constraints

  This question evaluates quantitative skills in pricing optimization, constrained investment allocation, and interpretation of willingness-to-pay curves, testing competency in combining economic reasoning with statistical and mathematical modeling.

  Statistics & MathHR Screen
• Capital OneMedium·Data Scientist
  Sketch function from derivatives and limits

  This question evaluates understanding of calculus concepts—derivatives, concavity, limits, and continuity—and the ability to interpret derivative sign patterns to infer monotonicity and locate extrema.

  Statistics & MathTechnical Screen
• CCargurusMedium·Data Scientist
  Assess a Distribution and Derive Coin-Toss Expectations

  This problem tests the ability to distinguish between Bernoulli and Binomial processes, calculate expected values and variances, and validate model assumptions based on observed sample data.

  Statistics & MathTechnical ScreenProbabilityStatisticsMLE
• CCiscoHard·Software Engineer
  Formalize a Minimum-Trip Transport Puzzle with Horses and Ladders

  Model a horses-and-ladders transport puzzle by clarifying legal moves, tracking resource state, and proving a minimum-trip plan is optimal.

  Statistics & MathTechnical Screen
• CitadelMedium·Data Scientist
  Calculate Probability of Third Card Being an Ace

  Evaluates conditional probability with cards drawn without replacement after observing at least one Ace. Strong answers define the conditioning event, account for the number of Aces among the first two cards, and compute the probability that the third card is an Ace as 49/825.

  Statistics & MathTechnical Screen
• CitadelMedium·Software Engineer
  Choose 200 of a Million Records to Label, Improving on Uniform Random Sampling

  Tests the ability to define data informativeness under extreme budget constraints (selecting 200 out of 1,000,000 records) and design a scalable, one-shot sampling strategy that outperforms uniform random sampling in coverage and diversity.

  Statistics & MathTechnical ScreenActive LearningSamplingClustering
• CitadelMedium·Data Scientist
  Compute P(third Ace | Ace in first two)

  This question evaluates understanding of conditional probability, dependence versus independence, symmetry arguments, and combinatorial reasoning in sampling without replacement.

  Statistics & MathTechnical Screen
• CitadelHard·Software Engineer
  Compute Statistics from a Frequency Array

  Compute count, minimum, maximum, mean, median, mode, and population standard deviation directly from a 256-bin frequency array. Use weighted moments and cumulative ranks without expanding samples, define empty-data behavior and ties, and address overflow and numerical precision.

  Statistics & MathTechnical Screen
• CitadelMedium·Data Scientist
  Compute variance of trading profits

  This interview question evaluates statistical assumptions, formulas, estimation strategy, uncertainty, edge cases, and interpretation in a realistic interview setting. A strong answer for Compute variance of trading profits states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

  Statistics & MathTechnical Screen
• CitadelMedium·Data Scientist
  Derive Coefficient and Covariance in Regression Analysis

  Evaluates statistics fundamentals across equicorrelation constraints, reverse regression slopes, covariance of uniform order statistics, and change of variables. Strong answers use positive semidefinite matrices, simple-regression identities, order-statistic expectations, and Jacobian transformations.

  Statistics & MathTechnical Screen
• CitadelEasy·Data Scientist
  Diagnose and Validate a Regression Model

  Work through regression model validation from split design and leakage prevention to residual analysis and segment-level error checks. The solution explains MAE versus RMSE, multicollinearity, coefficient limits, and when added model complexity is worth the operational cost.

  Statistics & MathTechnical Screen
• CitadelMedium·Data Scientist
  Explain multicollinearity and OLS assumptions

  Explain multicollinearity and OLS assumptions evaluates statistical assumptions, formulas, estimation strategy, uncertainty, edge cases, and interpretation in a realistic interview setting. A strong answer states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

  Statistics & MathTechnical Screen
• CitadelEasy·Data Scientist
  Find constant minimizing absolute error

  This question tests the understanding of L1 loss minimization and the statistical property that the median is the optimal point estimator under absolute error loss.

  Statistics & MathTechnical ScreenStatisticsOptimizationMedian
• CitadelHard·Data Scientist
  Solve Classic Probability Questions

  This problem tests your ability to calculate the expected stopping time of a stochastic process and your proficiency with the linearity of expectation in the context of sequential probability.

  Statistics & MathOnsiteProbabilityExpectationStochastic Processes
• CitadelHard·Data Scientist
  Solve probability and expectation problems

  This set of problems evaluates probabilistic reasoning and expectation skills across discrete and continuous settings, covering conditional probability with evolving information, convolution and distribution derivation, occupancy/collector problems, symmetry-based variance on manifolds, and sequential selection/optimal stopping.

  Statistics & MathOnsite
• CitiMedium·Software Engineer
  Solve two logic brain teasers

  This pair of puzzles evaluates logical deduction and optimization competencies—one testing information-theoretic reasoning with constrained ternary comparisons and the other testing sequencing and scheduling trade-offs for minimal total time—and belongs to the Cognitive Ability / Logic category.

  Statistics & MathOnsite
• CCitibankMedium·Data Scientist
  Compute expected payoff of reroll dice game

  This question evaluates understanding of probability theory and expected-value computation in stopping-time processes, including conditioning and infinite-series reasoning, and also tests modeling of per-trial costs and break-even analysis.

  Statistics & MathOnline Assessment
• CCitibankMedium·Data Scientist
  Price options and bonds via binomial no-arbitrage

  This question evaluates competence in no-arbitrage pricing, risk-neutral valuation, early-exercise features of American versus European options, and short-rate tree bond valuation within the Statistics & Math domain.

  Statistics & MathOnline Assessment
• CoinbaseMedium·Data Scientist
  Calculate Conversion Lift CI

  This question tests the ability to derive and calculate a confidence interval for the difference in conversion rates between two groups, and to explain how this interval informs a business decision.

  Statistics & MathOnsiteStatisticsA/B TestingInference