Statistics Interview Questions
Statistics is where data becomes a decision. This playlist takes you from the core machinery of inference -- maximum likelihood, confidence intervals, hypothesis testing, and Bayesian updating -- through the distribution toolkit (t, F, chi-squared, KS) and into the inference problems quants actually
How to think about statistics questions
Statistics is the inverse of probability: you see the data and must reason back to the mechanism that produced it. Nearly every problem is one question in disguise — what's my best guess for the unknown, and how much should I trust it?
ESTIMATE BY LIKELIHOOD
Given data, the most-defensible parameter is usually the one that makes what you saw most probable. Maximum likelihood formalizes that instinct, and a good estimator is judged on two axes: is it centered on the truth (unbiased), and how tightly does it cluster (low variance)?
SIGNAL VERSUS NOISE
A hypothesis test is just asking whether an effect is large relative to its own wobble. Standardize the estimate by its standard error and you get a number you can put a p-value on — and the bias–variance trade-off explains why the “best” estimator deliberately accepts a little bias to cut variance.
Work this set and one habit sticks: every answer is an estimate plus an honest measure of how much it could be wrong.
Statistics questions (100)
- MLE for a Bernoulli Parameter
- Correct Interpretation of a Frequentist Confidence Interval
- Bayesian Posterior for a Bernoulli Parameter
- Normal MLE for the Mean (Known Variance)
- Statistical Significance vs. Power
- Optimal Predictors Under Squared and Absolute Loss
- Correlation After Duplicating a Dataset
- Computing a 95% Confidence Interval
- Fisher Information for Exponential Samples
- Simpson's Paradox in Shot Accuracy
- Hypothesis Test for M&M Blue Proportion
- MLE for the Pareto Distribution
- Why We Divide by n-1 in Sample Variance
- t-Test for ETF Premium Persistence
- IQ and Motivation: Collider Bias in Subgroup Correlations
- Cross-Entropy, KL Divergence, and Jensen's Inequality
- Pooled-Variance Two-Sample t-Test
- Monte Carlo Pi Estimation and the German Tank Problem
- Chi-Squared Test for Flavor Preference Across Age Groups
- F-Test for Bolt Diameter Variance
- Factors That Do Not Affect Test Power
- Interpreting Rejection of the Null in OLS
- Referendum Confidence Interval and Passage Probability
- 90% Confidence Intervals: Calibration Exercise
- Which Coin Is More Biased?
- Optimal Estimate from Two Scales
- Bayesian A/B Test for Conversion Rates
- Welch's t-Test for Difference in Means Under Heteroskedasticity
- Optimal Weights for Combining Unbiased Estimators
- Beta-Bernoulli Posterior and Predictive Distribution
- Hypothesis Testing: Z-Score, Type II Error, and Sample Size
- James-Stein Shrinkage for Cross-Sectional Returns
- German Tank Problem
- Bayesian Update from a No-Trade Event
- Sample Size for Detecting a Biased Coin
- MLE for Uniform Distribution
- Correlation in Split Samples
- Experiment Design for Policy Impact
- Isotonic Regression and the Pool-Adjacent-Violators Algorithm
- Comparing Estimators for the Uniform Mean
- Disease Testing and Hypothesis Testing
- Prediction Intervals vs. Confidence Intervals in Regression
- Order Statistics and Inverse Transform Sampling
- Confidence Interval with Zero Successes
- Out-of-Sample R-Squared
- Size-Biased Sampling and the Harmonic Mean Correction
- Bayesian Credible Interval for Coin Bias
- Ljung-Box Test for Serial Correlation in Returns
- Confidence Intervals for Logistic Regression Parameters
- Confidence Interval for a Coin-Flip Game Price
- Blocked Randomization for Causal Inference
- Breusch-Godfrey Test for Serial Correlation
- False Discovery in Alpha Mining
- Online Mean and Variance for Streaming Returns
- Evaluating Probabilistic Weather Forecasters
- Testing for Heavy Tails in Index Returns
- Optimal Experiment Design for Comparing Two Coins
- Online Outlier Detection in a Data Stream
- Classification Calibration and Platt Scaling
- MLE, Confidence Interval, and Bayesian Posterior for a Coin
- Bias From Reusing Data in Hyperparameter Search
- LAD Estimator as MLE Under Laplace Errors
- Benjamini-Hochberg Procedure for Correlated Alpha Signals
- Dirichlet-Multinomial Posterior and Prediction
- VaR and ES via Peaks-Over-Threshold
- Hansen's Superior Predictive Ability Test
- Bayesian Coin: Posterior, Predictive, and Betting Decision
- MLE for GBM Drift and Volatility
- Type I and Type II Error Trade-off in a Gaussian Z-Test
- Multiple Testing and False Discovery in Alpha Backtesting
- Newey-West HAC Estimator in AR(1) Noise
- Normal-Normal Bayesian Updating with Known Variance
- Benjamini-Hochberg FDR Control
- Sample Size Derivation via CLT
- Gamma-Poisson Conjugate Updating
- Sequential A/B Testing via Wald SPRT
- Chi-Square Confidence Interval for Variance and Sample Sizing
- White's Reality Check for Data Snooping Across Multiple Strategies
- Comparing Two Poisson Rates
- Tail Risk Comparison Across Risk Measures
- Sequential A/B Testing With Alpha-Spending Functions
- Bayes Factor for Normal Mean With Directional Betting
- Two-Sample Kolmogorov-Smirnov Test
- Online Covariance and Correlation (Welford-Style)
- Bayesian Change-Point Detection in Mean
- ROC AUC as the Wilcoxon-Mann-Whitney Statistic
- Winsorization Impact on OLS
- Time-Series Mean Reversion Test
- Bayes-Optimal Decision Rule Under a Hidden Regime
- Multiple Testing: Max of 500 Null t-Statistics
- Estimation with Equicorrelated Normal Samples
- Hypothesis Test for Drift in a Brownian Motion
- Hill Estimator and Extreme Quantile Confidence Intervals
- Breusch-Pagan Heteroskedasticity Test
- Power and Sample Size for Sharpe Ratio Detection
- VaR Backtesting: Kupiec and Christoffersen Tests
- Estimating Informed-Flow Share via EM
- Asymptotic Distribution of the Sharpe Ratio
- MLE for Student-t Location-Scale via IRLS
- GMM Estimation of CAPM Beta
Statistics interview questions FAQ
What kind of statistics questions show up in quant interviews?
This page collects 100 statistics problems that recur in quant trading and research interviews, each with a full worked solution and the intuition behind it. They range from quick warmups to the harder variants firms use to separate candidates.
How hard are statistics interview questions?
The set spans 15 easy, 54 medium and 31 hard problems. Most sit at medium difficulty — a few minutes of clean reasoning — with a harder tail that rewards knowing the canonical approach rather than grinding.
How should I practice statistics for quant interviews?
Work through them by difficulty, starting just below your level, and write the solution out before checking. 13 are free to open with the full worked solution, so you can judge the quality first. Focus on the recurring patterns rather than memorizing answers — the same handful of ideas generate most variants.
Are these real quant interview questions?
They are a curated set drawn from our problem bank — the kind of statistics question that actually appears in quant interviews, rewritten for clarity with solutions we author ourselves. We don't claim any single wording is verbatim, and every problem carries a full solution.