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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Compute probability at least one user uses feature
Problem Assume there are \(n\) users. Each user independently uses a certain feature with probability \(p\). 1) What is the probability that at least ...
Write the logistic regression loss function
Logistic Regression Loss Consider binary logistic regression. - Dataset: \(\{(\mathbf{x}_i, y_i)\}_{i=1}^n\) - Labels: \(y_i \in \{0,1\}\) - Model: \(...
Compute negative-price probability after n steps
Random-Walk Price Crossing Probability Setup - Initial price: S₀ = s (real number). - Step size: x > 0. - Number of days: n (integer ≥ 0). - Each day ...
Determine Appropriate Statistical Test for Comparing Means
A/B Test: Active Minutes After Two Weeks Scenario You ran a two-week A/B experiment on a new algorithm. The primary metric is user active minutes. Ass...
Solve probability and expectation problems
Probability and Statistics Mini-Set Context: Answer each item independently. Unless otherwise specified, assume independence and uniform randomness; d...
Differentiate sample vs population standard deviation
Population vs. Sample Standard Deviation in a Finite Rolling Window Context You are implementing a rolling standard deviation over a fixed-size window...
Differentiate fixed and variable costs with examples
Unit Economics: Fixed vs. Variable Costs in a Subscription Streaming Business Task - Define fixed cost vs. variable cost for a subscription streaming ...
Compute precision under noisy annotators
Two-Annotator Labeling Policy: Precision, Recall, F1, and Generalization You have two independent annotators who review videos and label them as "ille...
Test a coefficient and explain t-distribution
In OLS, test whether feature j is relevant. a) State H0: β_j = 0 versus H1: β_j ≠ 0 and construct the t‑statistic t_j = b̂_j / se(b̂_j), giving the ex...
Define and sample a truncated normal
Define the truncated normal Z | a < Z < b for Z ~ N(0,1): write the normalized pdf and cdf. Then design efficient samplers for three cases: (i) a = 1,...
Compute robust linear interpolation with edge cases
You are given two distinct points (x0, y0) and (x1, y1) with x0 != x1. a) Derive the linear interpolation function f(x) on [min(x0, x1), max(x0, x1)] ...
Apply sequential testing without p-hacking
Sequential Monitoring With Early Stopping Context: You are planning a two‑sided hypothesis test with continuous monitoring and early stopping for effi...
Contrast OLS, DiD, and PSM assumptions
For the shuttle impact problem, contrast OLS, DiD, and PSM rigorously. Do the following: 1) write the OLS and two-way fixed-effects DiD regression equ...
Compute profit and decompose Groupon impact
You run a restaurant with these economics: baseline demand is 20 tables/day, average revenue is $30/table, variable cost (VC) is 40% of revenue, and f...
Simulate via inverse transform and Gibbs
Inverse transform: (a) Derive an algorithm to simulate from the Logistic(μ, s) distribution using its CDF and inverse CDF; show how to obtain samples ...
Optimize profitability for coding contract decisions
A client offers two mutually exclusive fixed-price projects starting 2025-10-01 with a hard deadline of 2025-10-31. Your current team has 3 engineers....
Interpret regression metrics and assumptions
A multiple linear regression is fit to predict arrival delay with standardized numeric predictors and one‑hot categorical variables. Without seeing th...
Choose tests under non‑normal, unequal variance
Heavy-Tailed, Heteroskedastic Metrics in A/B Tests (AOV example) Context: You are comparing two groups in an A/B test on a spend metric (e.g., Average...
Compute A/B sample size under clustering
A/B Test Sample Size With Unequal Allocation, Clustering, and Attrition Context You are planning a two-arm signup A/B test (binary outcome: convert vs...
Analyze skewed comments and sampling effects
Right‑Skewed Daily Comments: Location Stats and Sampling Distributions You’re analyzing daily user comments per user, which are right‑skewed count dat...