Statistics & Math Interview Questions

Showing 121–150 of 439 results

• GleanMedium·Data Scientist
  Expectation and Variance of a Sum of Two Random Variables, Including Covariance

  Asks how to compute the expectation and variance of the sum of two random variables, in general and when they are independent. Tests derivation from definitions, the role of covariance, generalizing to weighted sums and differences, and applying the result to data-science problems such as comparing group means.

  Statistics & MathOnsite
• GleanEasy·Data Scientist
  What are sum expectation and variance?

  This question evaluates understanding of expectation, variance and covariance and the ability to reason about how sums of random variables affect their moments, including the role of covariance and the special case of independence in the Statistics & Math domain.

  Statistics & MathOnsite
• Goldman SachsEasy·Data Scientist
  Bound the Rank of BA Given Rank of AB

  Determine the set of possible values for the rank of the matrix product BA given that A and B are 4x4 real matrices and rank(AB) = 2. This question tests fundamental linear algebra inequalities involving matrix ranks and nullities.

  Statistics & MathOnline AssessmentLinear AlgebraMatrix TheoryRank Inequalities
• Goldman SachsEasy·Data Scientist
  Compute the Arc Length of a Curve

  Tests single-variable calculus fundamentals, specifically calculating the derivative, setting up the standard arc length integral, and evaluating it using substitution.

  Statistics & MathOnline Assessmentcalculusintegrationgeometry
• Goldman SachsMedium·Quantitative Researcher
  Estimate Pi with a Square Cardboard and a Fair Die to 5-6 Decimal Places

  Using only a square piece of cardboard and a fair six-sided die, design an experiment that estimates pi empirically, then explain how many trials 5 to 6 correct decimal places would require and how you would get there. It tests Monte Carlo design, bias versus variance, and error analysis.

  Statistics & MathTechnical Screen
• Goldman SachsEasy·Data Scientist
  Expected Number of Runs in Coin Tosses

  Tests understanding of linearity of expectation and indicator random variables through counting consecutive runs in a sequence of coin tosses.

  Statistics & MathOnline Assessmentprobabilityexpected-valuecombinatorics
• Goldman SachsMedium·Quantitative Researcher
  From Alpha Signal to Portfolio: Reliability, Regime Dependence and Entropy

  Walk through how a quantitative equity team turns a predictive signal into portfolio holdings, then explain how to judge whether the signal is reliable, whether its performance depends on the market regime, and how entropy and mutual information can be used to evaluate signals and portfolios.

  Statistics & MathTechnical Screen
• Goldman SachsEasy·Data Scientist
  Infer BA When AB Is the Identity

  This question tests the understanding of matrix invertibility, the properties of the identity matrix, and the fundamental differences between square and non-square matrix multiplication.

  Statistics & MathOnline AssessmentLinear AlgebraMatricesRank
• Goldman SachsEasy·Data Scientist
  Integrate a Two-Sided Exponential Density

  This question tests the ability to integrate probability density functions (PDFs) over specified intervals, specifically handling the absolute value function in symmetric distributions.

  Statistics & MathOnline AssessmentCalculusProbabilityDistributions
• GoogleMedium·Data Scientist
  Analyze Linear Regression Changes with Duplicated Observations

  Evaluates regression and hypothesis-testing interpretation under duplicated observations and large samples. Strong answers show unchanged OLS coefficients, standard-error effects, p-value meaning, and practical chi-square adjustments.

  Statistics & MathTechnical Screen
• GoogleMedium·Data Scientist
  Analyze data duplication effects in linear regression

  This question evaluates understanding of OLS estimation, the effects of duplicated observations on estimator variance and inference, and the interplay between sample size, p-values, and effect-size measures within the Statistics & Math domain for a Data Scientist role.

  Statistics & MathTechnical Screen
• GoogleMedium·Data Scientist
  Approximate a percentile from buckets

  This question tests the ability to interpolate values within histogram buckets to estimate a specific percentile, requiring an understanding of linear versus log-space assumptions.

  Statistics & MathTechnical ScreenStatisticsEstimationAlgorithms
• GoogleMedium·Data Scientist
  Assess Fundamental Statistics Knowledge in Data-Science Interviews

  Google data scientist statistics prompt covering MLEs for normal mean and variance, conditional density from a joint pdf, standard normal pdf and cdf, and assumptions for unbiased estimators.

  Statistics & MathTechnical Screen
• GoogleMedium·Data Scientist
  Can bootstrap help reduce variance

  This question evaluates understanding of bootstrap resampling, the distinction between estimating an estimator’s variance and methods that actually reduce estimator variance, and related ensemble reasoning for a Data Scientist role in the Statistics & Math domain.

  Statistics & MathOnsite
• GoogleMedium·Data Scientist
  Derive MLEs and conditional Normal distributions

  This question evaluates proficiency in parametric inference and probability theory, specifically maximum likelihood estimation, bias of estimators, and conditioning in univariate and bivariate Normal distributions including constrained estimation of parameters.

  Statistics & MathTechnical Screen
• GoogleHard·Data Scientist
  Design human review to estimate model accuracy

  This interview question evaluates statistical assumptions, formulas, estimation strategy, uncertainty, edge cases, and interpretation in a realistic interview setting. A strong answer for Design human review to estimate model accuracy states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

  Statistics & MathOnsite
• GoogleMedium·Data Scientist
  Determine Impact of New Chat-Notification on User Engagement

  Determine Impact of New Chat-Notification on User Engagement 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
• GoogleEasy·Data Scientist
  Determine Normality of Single Observation with Z-Test

  Evaluates hypothesis testing for a single observation against a fully specified standard normal distribution. Strong answers state hypotheses, use z = x, define critical values and p-values, and note limitations.

  Statistics & MathTechnical Screen
• GoogleHard·Data Scientist
  Estimate Population Mean and Conversion Rate Accurately

  Evaluates core statistical inference skills across p-values, confidence intervals, standard error reduction, tail probability estimation, efficient conversion-rate sampling, and truncated-normal estimation. Strong answers state assumptions, use appropriate intervals and weights, and avoid common interpretation errors.

  Statistics & MathOnsite
• GoogleMedium·Data Scientist
  Estimate percentile from buckets

  Estimate a percentile from histogram buckets by locating the cumulative-count bucket, explaining why midpoint can be poor, interpolating within the bucket under explicit assumptions, handling log-spaced buckets and edge cases, and reporting uncertainty when buckets are coarse.

  Statistics & MathTechnical Screen
• GoogleMedium·Data Scientist
  Estimate population singletons from a 10% log

  This question evaluates mastery of statistical estimation and sampling theory, including recognition of bias from subsampling, frequency‑of‑frequencies modeling for rare events, uncertainty quantification under heavy‑tailed counts, and design of simulation studies.

  Statistics & MathTechnical Screen
• GoogleMedium·Data Scientist
  Estimate unbiased ad scores with many reviewers

  This problem tests the ability to design an estimation framework that accounts for rater bias and variance, specifically applying concepts like hierarchical modeling or fixed-effect normalization to estimate latent variables.

  Statistics & MathTechnical ScreenStatisticsModelingBias
• GoogleEasy·Data Scientist
  Estimate weather’s effect on mental health

  This problem tests the ability to design an observational study to measure the causal impact of meteorological variables on self-reported mental health scores, focusing on confounding variables and identification strategies.

  Statistics & MathHR ScreenCausal InferenceRegressionConfounding
• GoogleHard·Data Scientist
  Explain Bootstrap and Prove Uniformity

  This question tests the conceptual understanding of bootstrap resampling for variance estimation and the mathematical proof of probability distributions using the properties of the Uniform distribution.

  Statistics & MathTechnical ScreenStatisticsProbabilityBootstrap
• GoogleHard·Data Scientist
  Explain Bootstrap and Statistical Inference

  This problem tests your understanding of bootstrap resampling theory, confidence interval construction, and the statistical trade-offs involved in hypothesis testing for small-sample experiments.

  Statistics & MathTechnical ScreenBootstrapHypothesis TestingMLE
• GoogleMedium·Data Scientist
  Explain P-values and Confidence Intervals in Simple Linear Regression

  Review p-values, confidence intervals and slope inference in simple linear regression, including assumptions and causal limits.

  Statistics & MathOnsite
• GoogleMedium·Data Scientist
  Explain Simpson’s Paradox and Its Causes with Example

  Evaluates Simpson's paradox through definition, confounding, subgroup imbalance, and a numeric reversal example. Strong answers compare stratified and aggregate rates and explain when each comparison matters.

  Statistics & MathTechnical Screen
• GoogleMedium·Data Scientist
  Explain and resolve Simpson’s paradox

  This question evaluates understanding of Simpson's paradox, confounding, and causal reasoning, checking numerical interpretation of subgroup versus aggregate statistics and the ability to recognize when aggregated averages can mislead.

  Statistics & MathTechnical Screen
• GoogleEasy·Data Scientist
  Explain mixed models and fixed vs random effects

  This question evaluates understanding of mixed effects models, the conceptual distinction between fixed and random effects, interpretation of coefficients and variance components, and awareness of practical pitfalls when modeling hierarchical or panel data.

  Statistics & MathOnsite
• GoogleMedium·Data Scientist
  Generate Samples from Truncated Normal Distribution

  Evaluates truncated normal distribution fundamentals and sampling methods for lower-tail truncation. Strong answers name the lower-truncated normal, provide the PDF and CDF, and compare inverse-CDF, rejection, and tail-efficient samplers.

  Statistics & MathTechnical Screen