Statistics & Math Interview Questions
Practice 482 real Statistics & Math interview questions for 2026 — Statistics & Math interview questions gathered from actual interviews, with detailed solutions to guide your interview preparation. Covers companies like Meta, Capital One, Google, Amazon, and Optiver and roles such as Data Scientist, Quant/Trader, ML researcher, and Data Analyst. This collection is distinctive because problems range from applied inference

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"I recently cleared Uber interviews (strong hire in the design round) and all the questions were present in prachub."
"The search is what sold me. I typed in a really niche DP problem I got asked last year and it actually came up, full breakdown and everything. These guys are clearly updating it constantly."
Describe Facebook User Comment Distribution Shape and Justification
Characterizing Comments per User on Facebook Context You are analyzing the number of comments made by each user over a fixed time window (e.g., 30 day...
Estimate and Derive Regression Coefficient for X on y
Statistics & Probability Onsite — Two-Part Question Context - You have a simple linear data-generating process: y = X + ε, where X and ε are independe...
Calculate Conversion Probability for Male Ad Impressions
Scenario You are estimating conversion probabilities for ad impressions. Before knowing a user's gender, the overall conversion rate is 2%. Given - P(...
Prove Equal Probability Impossible with Relabeled Dice Faces
Uniform Sums from Two Relabeled Fair Dice Setup You have two fair six-sided dice. You may relabel each die's faces with integers; duplicates are allow...
Evaluate Probability of Positive User Comments and Model Performance
Social-Media Positivity: Independence and Model Comparison Context You are evaluating user comment sentiment and the performance of two models that cl...
Test Whether Two Samples Come From the Same Distribution
Question You have two datasets, sample A and sample B. They might come from two versions of a system, two cities, or two periods of autonomous-driving...
Compute unit economics and insurance break-even
Subscription unit economics and insurance math. Assume no discounting and ignore taxes unless stated. Part A (15-month term): A subscription service c...
Test if one value comes from N(μ,σ²)
Assume the population is N(μ, σ²) with μ and σ known. You observe a single value x = 1.37. Formulate a two-sided hypothesis test H0: X ~ N(μ, σ²) vs H...
Plan and analyze an A/B test
A/B Test: Power, Clustering, Sequential Monitoring, Multiple Comparisons, and Diagnostics Context You are planning an A/B test for a dashboard change ...
Control error under multiple testing
Multiple Testing and Sequential Monitoring with 1 Primary and 12 Secondary Metrics Context You are monitoring an A/B experiment over 4 weekly looks. T...
Relate Y-on-X and X-on-Y coefficients
Relating Slopes When Reversing Simple Linear Regression Context You fit an ordinary least squares (OLS) simple linear regression with an intercept of ...
Derive lower bound for equicorrelation rho
Equicorrelation Matrix PSD Condition Setup Consider zero-mean, unit-variance random variables whose pairwise correlations are all equal to a common va...
Compare solar vs biomass paybacks and recommend
Compare two investments. Assume all energy prices/costs are per MWh and the selling price is $40 per MWh. Project A (Solar): initial investment = $12....
Analyze ad targeting expectations and distributions
Ads Profit, Variance Decomposition, and Exponential Timing Context: You run an ad slot with two user segments. On each eligible page view (impression ...
Compute p-values and adjust multiplicity
You test if a coin is fair after 20 flips and observe 17 heads. (a) Compute the exact two-sided p-value under a Binomial(20, 0.5) model. (b) Approxima...
Analyze omitted-variable bias in regression
Omitted-Variable Bias, Heteroscedasticity, and Remedies Setup - True data-generating process (DGP): Y = β0 + β1·Temp + β2·Occupancy + ε - Assumption...
Design cross-validation; explain bias–variance
Define cross-validation rigorously and compare k-fold, stratified k-fold, leave-one-out, nested CV, and time-series rolling/blocked CV. For a dataset ...
Define and compute surge pricing metrics
Surge Pricing Metrics, Formulas, and Causal Estimation You are evaluating surge pricing in a two-sided marketplace (customers place requests; drivers/...
Quantify launch decision with tests and guardrails
You will formalize the statistical decision rules for the Instagram button experiment described above. Given: baseline exploration rate (p0) = 0.15 pe...
Derive paying users over time with churn
Leaky-Bucket Model of Paying Users Context - Time is discrete by month t = 1, 2, ... - Each month t: - N new users start a free trial. - a (fracti...