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

"I got asked a hardcore MCM DP question and I saw it on PracHub as well. Solved that question in 5 minutes. Without PracHub I doubt I could solve it in 5 hours. Though somehow didn't get hired, perhaps I guess I solved it too fast? /s"

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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."
Explain and resolve Simpson’s paradox
Define Simpson’s paradox and construct a concrete numeric example where group-wise success rates favor treatment in each subgroup but the aggregate ra...
Test conversion difference and adjust for clustering
Using aggregated results for the 7‑day window 2025‑08‑26..2025‑09‑01, evaluate statistical significance and power for conversion uplift, accounting fo...
Solve probability and expectation problems
Probability and Expectation Practice (Take‑home) Assume all coins and dice are fair unless stated otherwise. Show reasoning and final results. 1) Thre...
Model wins-until-failure and expected future wins
You are given a DataFrame df where each row summarizes a player’s performance until their first loss. Input df columns: - player_id (string/int) - win...
Derive mean and variance of x̄
Let \(X_1, X_2, \dots, X_n\) be random variables, and define the sample mean as \(\bar X = \frac{1}{n}\sum_{i=1}^n X_i\). 1. Assume the variables are ...
Solve numeric sequence pattern puzzles
Sequence Pattern Puzzles This is a timed pattern-recognition section of the kind used on quantitative-trading aptitude tests. You are given five indep...
Diagnose and fix multicollinearity in income regression
You want to estimate the relationship between gender and income using a regression model, while controlling for other covariates such as: - age - educ...
Relate coefficients under linear feature transformation
Answer both parts. Part 1: Coefficients under feature transformation You have original predictors \(x_1, x_2\) and define transformed predictors: - \(...
Explain and derive importance sampling estimators
Importance Sampling: Estimators, Properties, Optimal Proposals, and ESS Context You want to estimate an expectation under a target distribution p over...
Calculate conditional probabilities for coin tosses
Probability with Two Fair Coin Tosses You toss a fair coin twice. Let the coin be fair (P(H) = P(T) = 1/2) and the tosses independent. (a) Compute P(s...
Derive MLEs and conditional Normal distributions
Normal and Bivariate Normal: PDFs/CDFs, MLEs, Conditioning, and Unbiased Variance Setup - Let X1, …, Xn be i.i.d. Normal(μ, σ²). - Independently, let ...
Compute averages and binomial/Poisson probabilities
Streaming Mean and Binomial vs Poisson Approximation Part A — Streaming Mean Update You have an existing dataset of N = 1,000 observations with mean 1...
Compute sample size and analyze A/B results
A/B Test: Sample Size, Sequential Correction, and Post-Experiment Analysis Context You are planning a two-arm A/B test with a binary (Bernoulli) conve...
Solve Market-Risk and Probability Questions
Question Answer the following quantitative interview questions for a market-risk / data-scientist screen at Morgan Stanley. 1. Stress testing WTI and ...
Estimate total attendance from size-biased reservation sample
You run a restaurant with N = 10,000 reservations in a day. Each reservation j has: - Reserved party size: \(R_j\) (positive integer) - Actual number ...
Analyze EV, arbitrage, and bet sizing across games
Betting Games: EV, Variance, Arbitrage, and Sizing Context You will be shown payout tables or odds for three independent games. Your task is to quickl...
Compute Optimal Die Re-roll Strategy
A fair six-sided die pays its face value in dollars. You may roll up to three times total. - After the first or second roll, you may either keep the o...
Find next terms in sequences
Pattern Recognition: Find the Rule and Next Term You are given 8 number sequences. For each sequence: - Identify a clear rule that generates the terms...
Should you play a dice payout game?
Two players each roll a fair six-sided die once. - If you win (your roll > opponent’s roll), the opponent pays you $n. - If the opponent wins or it’s ...
Model network-service unit economics and breakeven
A network service charges $40/month with the first 3 months free. Costs: variable service cost $25 per active month; one-time install cost $35 at acti...