Interview questions
Statistics quant interview questions
57 interview-style statistics problems, ordered from easy to hard.
Statistics interview questions appear in quant research, data science and systematic trading interviews. They check whether you understand estimators, confidence intervals, hypothesis tests, regression assumptions, correlation versus causation and the behaviour of sums of random variables via the central limit theorem. Interviewers also probe intuition: what happens to a regression coefficient when you add a correlated variable, or how many samples you need to detect an edge. The problems here progress from distribution facts and estimation to modelling questions with realistic data issues such as bias, overfitting and multiple testing. Free problems come with hints and worked solutions that state their assumptions clearly. Practise them interactively to measure your accuracy, and pair them with the statistics lessons and cheat sheets when a concept needs revision.
Practice Statistics interactivelyEasy (21)
- Precision of the Mean · Estimation
- Sum of Independent Normals · Normal Distribution
- Population Regression Coefficient · Linear Regression
- Eigenvalues of a Symmetric 2x2 Matrix · Linear Algebra
- Rank of an Outer Product · Linear Algebra
- Minimum Norm Under a Linear Constraint · Optimization
- Sum of Two Independent Normals · Normal Distribution
- Linear Transformation of a Normal · Normal Distribution
- MLE of a Bernoulli Parameter · Maximum Likelihood
- MLE of a Normal Mean · Maximum Likelihood
- Variance of the Sample Mean · Sampling Distributions
- Large-Sample Distribution of the Sample Mean · Central Limit Theorem
- Posterior Mean of a Beta Distribution · Bayesian Inference
- Mean and Variance of a Poisson · Discrete Distributions
- Mean and Variance of an Exponential · Continuous Distributions
- Mean of a Geometric Waiting Time · Discrete Distributions
- Mean of a Uniform Distribution · Continuous Distributions
- Variance of a Uniform Distribution · Continuous Distributions
- One-Day Value at Risk, Second Instance · Risk · Value at Risk
- Mean of Four Numbers · Descriptive Statistics
- Variance of a Coin Indicator · Bernoulli
Medium (29)
- Covariance With a Sum · Covariance
- Correlated Sum Variance · Correlation
- Two Million VaR · Risk · Value at Risk
- Zero Covariance Without Independence · Dependence
- Beta-Binomial Posterior Update · Bayesian Statistics
- Positive Definiteness of a 2x2 Symmetric Matrix · Linear Algebra
- Orthogonal Projection onto a Line · Linear Algebra
- Eigenvalues From Trace and Determinant · Linear Algebra
- Cobb-Douglas Resource Allocation · Optimization
- Gradient of a Quadratic Form · Linear Algebra
- Look-Ahead Bias in Backtesting · Backtesting
- Expected False Positives Under Multiple Testing · Hypothesis Testing
- Primary Effect of Severe Multicollinearity · Regression
- Why Shuffling Breaks Time-Series Cross-Validation · Model Validation
- Definition of Weak Covariance Stationarity · Time Series
- Why Selecting the Best Backtested Rule Overstates Performance · Backtesting
- Covariance of Two Linear Functions · Covariance
- Correlation Between a Variable and Its Sum · Correlation
- MLE of an Exponential Rate · Maximum Likelihood
- MLE Denominator for Normal Variance · Maximum Likelihood
- Beta-Bernoulli Posterior Update · Bayesian Inference
- CDF of the Maximum of Uniforms · Order Statistics
- Expected kth Order Statistic of Uniforms · Order Statistics
- Law of Total Expectation Application · Conditional Expectation
- Binomial Mean and Variance · Binomial
- Poisson Zero · Poisson
- Normal Below Its Mean · Normal
- Variance of a Difference · Variance
- Correlation From Covariance · Correlation
Hard (7)
- MLE for Uniform Support · Estimation
- Total Variance Split · Law of Total Variance
- Minimum-Variance Portfolio Weight · Optimization
- Optimization Behind the First Principal Component · PCA
- Meaning of Cointegration · Time Series
- Law of Total Variance Application · Conditional Variance
- Variance of a Sample Mean · Sampling