Statistics & Math Interview Questions

Showing 121–150 of 218 results

• MercorMedium·Software Engineer
  Reason About Coffee-Quality Comparison Probabilities

  Calculate conditional comparison probabilities for coffee quality scores under continuous and discrete distributions, accounting for ties and sample permutations.

  Statistics & MathTechnical Screenprobabilitycombinatoricsstatistics
• MetaMedium·Data Scientist
  Compute and correct correlation significance inflation

  This question tests the understanding of how multiple hypothesis testing increases the risk of false positives (Type I error) in high-dimensional correlation matrices and requires the application of correction methods to maintain statistical integrity.

  Statistics & MathTechnical ScreenStatisticsHypothesis TestingCorrelation
• MetaMedium·Data Scientist
  Compute posterior fake probability using Bayes' rule

  The problem evaluates understanding of Bayes' rule and conditional probability within the Statistics & Math domain for a Data Scientist role, at an introductory applied probability/interpretation level.

  Statistics & MathTechnical Screen
• MetaEasy·Data Scientist
  Compute probability an account is fake

  This question tests the ability to apply Bayes' Theorem to update the probability of a hypothesis (an account being fake) given new evidence (an automated flag).

  Statistics & MathTechnical ScreenBayesian StatisticsConditional ProbabilityClassification Metrics
• MetaHard·Data Scientist
  Compute sample size and test duration correctly

  This question evaluates competency in experiment design and statistical power calculations, including sample size estimation, variance misspecification effects, multiple-comparison corrections, sequential monitoring boundaries, and adjustments for covariates or clustering.

  Statistics & MathTechnical Screen
• MetaMedium·Software Engineer
  Derive max distinct frequencies for n items

  The question evaluates combinatorial reasoning, discrete mathematics, and constructive extremal analysis by asking for the maximum number of distinct frequency counts in an array and a matching construction.

  Statistics & MathTechnical Screen
• MetaMedium·Data Scientist
  Estimate Portal’s causal lift on video-call usage

  This problem tests the ability to design an observational causal inference framework using Difference-in-Differences (DiD) in a setting with staggered adoption, specifically addressing selection bias and household-level measurement errors.

  Statistics & MathTechnical ScreenCausal InferenceDifference-in-DifferencesStaggered Adoption
• MetaHard·Data Scientist
  Estimate and validate weights for engagement actions

  This question tests the ability to derive an engagement scoring model, handle high-dimensional collinear features, and establish a robust validation framework for point-in-time predictions.

  Statistics & MathTechnical ScreenRegressionRegularizationMulticollinearity
• MetaMedium·Software Engineer
  Measure Forty-Five Minutes with Two Unevenly Burning Ropes

  Measure exactly 45 minutes using two ropes that each burn for 60 minutes but at unpredictable rates. The reasoning must rely only on lighting rope ends and observing completion events, never on assuming that half a rope represents half the time.

  Statistics & MathTechnical Screen
• MetaMedium·Data Scientist
  Model Unique Recipients with Poisson Distribution and Test Fit

  Evaluates statistical modeling of unique recipient counts per caller using count distributions. Strong answers compare Poisson, binomial, negative binomial, zero-inflated, and segmented models, then test fit with dispersion checks, likelihood metrics, chi-square tests, and simulation-based diagnostics.

  Statistics & MathTechnical Screen
• MicrosoftMedium·Data Scientist
  Choose Classification Metrics Under Asymmetric Costs

  This question evaluates understanding of binary classification evaluation metrics and model-operating decisions, covering confusion-matrix-derived measures (precision, recall/sensitivity, specificity, false positive/negative rates), summary metrics (ROC-AUC, PR-AUC), Type I/II errors, threshold selection, prevalence drift, probability calibration, and cost-sensitive trade-offs. It is commonly asked to assess a data scientist's ability to reason about model performance under class imbalance and asymmetric business costs, and it belongs to the Statistics & Math / Machine Learning model-evaluation domain requiring both conceptual understanding and practical application.

  Statistics & MathTechnical Screen
• MicrosoftEasy·Data Scientist
  Compute P(Bag B | red) via Bayes

  This question evaluates understanding of Bayes' rule and conditional probability by requiring computation of the posterior probability that a particular bag was chosen given a red draw.

  Statistics & MathTechnical Screen
• MicrosoftEasy·Data Scientist
  Use confusion matrix to choose model metric

  This question tests the ability to select appropriate classification metrics based on specific business objectives, asymmetric error costs, and dataset characteristics like class imbalance.

  Statistics & MathTechnical ScreenClassificationImbalanced DataEvaluation Metrics
• MMorningstarEasy·Data Scientist
  Explain a stochastic process simply

  This question assesses the candidate's ability to intuitively define a stochastic process, differentiate it from static probability models, and articulate fundamental properties like stationarity and the Markov property.

  Statistics & MathTechnical ScreenStatisticsStochastic ProcessesTime Series
• OneMain FinancialMedium·Data Scientist
  Differentiate and control Type I/II errors

  This question evaluates understanding of hypothesis testing fundamentals such as Type I/Type II errors, statistical power and sample size calculation for two-proportion tests, family-wise error rate control (e.g., Bonferroni), and sequential analysis/alpha-spending schemes.

  Statistics & MathTechnical Screen
• OneMain FinancialMedium·Data Scientist
  Maximize Probability of Drawing Two Red Balls

  This interview question evaluates statistical assumptions, formulas, estimation strategy, uncertainty, edge cases, and interpretation in a realistic interview setting. A strong answer for Maximize Probability of Drawing Two Red Balls states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

  Statistics & MathTechnical Screen
• OptiverHard·Data Scientist
  Analyze EV, arbitrage, and bet sizing across games

  This question evaluates proficiency in probability and statistics—particularly expected value and variance computation, arbitrage detection across payoff tables, quantitative bet-sizing strategies (e.g., Kelly and fractional sizing), and numerical approximation skills for independent discrete outcomes.

  Statistics & MathTechnical Screen
• OptiverHard·Software Engineer
  Analyze an Unfair-Coin Bankroll Game

  This problem tests probability theory and expected value calculations in the context of a game with an unfair coin and a bankroll constraint.

  Statistics & MathTechnical ScreenProbabilityExpected ValueRecurrence Relations
• OptiverHard·Software Engineer
  Calculate the Probability That Two Dice Sum to Seven

  This question tests fundamental understanding of discrete probability, combinatorics, and the impact of conditional dependencies on outcomes.

  Statistics & MathTechnical ScreenProbabilityCombinatoricsStatistics
• OptiverMedium·Software Engineer
  Compute expectations, conditionals, odds, and distributions

  This question evaluates proficiency in fundamental probability and statistics concepts — including expected value and variance, conditional probability, discrete arrival modeling, betting odds and the Kelly criterion, and combinatorics for draws without replacement — and is categorized under Statistics & Math.

  Statistics & MathTechnical Screen
• OptiverMedium·Data Scientist
  Compute expected coin flips to meet on octagon

  Compute expected coin flips to meet on octagon 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
• OptiverMedium·Software Engineer
  Demonstrate task switching and memory strategies

  This question evaluates task-switching ability, working-memory management, interference control, and error-recovery strategies—core executive functions involved in rapid stimulus–response mappings.

  Statistics & MathTechnical Screen
• OptiverMedium·Quantitative Researcher
  Design dice betting strategy under time limit

  This question evaluates probabilistic reasoning, expected-value computation, risk management and staking-strategy concepts including Kelly-style bet sizing, confidence-interval estimation, and return–variance trade-offs in the Statistics & Math domain.

  Statistics & MathTechnical Screen
• OptiverHard·Software Engineer
  Find the Color Probability After Discarding Cards

  This problem tests your understanding of conditional probability, combinatorics, and how dependent events (sampling without replacement) impact statistical expectations.

  Statistics & MathTechnical ScreenProbabilityCombinatoricsStatistics
• OptiverHard·Software Engineer
  Find the Probability That the Three Smallest Dice Sum to Three

  This problem tests combinatorics and probability theory by requiring the derivation of the exact probability that the three smallest values of four independent dice rolls sum to exactly three.

  Statistics & MathTechnical ScreenProbabilityCombinatoricsStatistics
• OptiverHard·Quantitative Trader
  Optimize interval-scoring strategy

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

  Statistics & MathTechnical Screen
• OOtherMedium·Data Scientist
  Compute and estimate Markov transition probabilities

  This question evaluates understanding of discrete-time Markov chains, multi-step transition probabilities and empirical estimation of transition matrices, testing probabilistic reasoning and matrix-based computation in the Statistics & Math domain for a Data Scientist role; it is commonly asked because it probes both theoretical grasp of stochastic processes and practical data-driven parameter estimation. At an applied algorithmic abstraction level, it requires explicit mapping of state labels to matrix indices, computing k-step transitions from a given row-stochastic matrix, estimating transition probabilities from observed one-step transitions, and addressing zero-outgoing-observation cases and any chosen smoothing policy (or justification for none).

  Statistics & MathTechnical Screen
• OOtherEasy·Data Scientist
  Compute multi-step Markov probabilities and estimate transitions

  This question evaluates understanding of discrete-time Markov chains, computation of multi-step transition probabilities from a one-step transition matrix, and empirical estimation of transition matrices from observed state-pair data including handling states with zero outgoing transitions.

  Statistics & MathTechnical Screen
• OOtherHard·Data Scientist
  Decide launch with p=0.10 at alpha 0.05

  This question evaluates a data scientist's competency in statistical inference and experiment decision-making, including frequentist hypothesis testing, conditional power and sample-size planning, Bayesian updating, and cost-sensitive risk analysis.

  Statistics & MathTechnical Screen
• OOtherMedium·Quantitative Researcher
  Optimal Stopping with a Ten-Sided Die and a Reset

  Derive optimal stopping thresholds for a fair ten-sided accumulation game, then account for the continuation value of a one-time zero reset.

  Statistics & MathTechnical Screen