Statistics & Math Interview Questions
Practice the exact questions companies are asking right now.
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Compute probability an account is fake
A platform uses an automated classifier to flag potentially fake accounts. Assume: - Base rate: 2% of accounts are fake. - The classifier flags a fake...
Explain why the t-statistic helps
Suppose you estimate an effect size \(\hat{\beta}\) in a regression model or an A/B test and compute a standard error \(SE(\hat{\beta})\). Explain why...
Answer core probability and statistics questions
Answer the following interview-style probability/statistics questions. Provide formulas and short explanations. 1) Bayes’ rule: State Bayes’ rule. Giv...
Why Use a t-Statistic?
In the context of an A/B test or a linear regression, explain why the t-statistic is a useful measure for evaluating whether an estimated effect diffe...
Correct length-biased sampling from family-size survey
In a town, you visit a school and ask 100 kids: “How many children are in your family?” You observe: - 50 kids say their family has 1 child - 20 kids ...
How compare Waymo turning trajectories statistically
Problem You have aerial-drone data that records the 2D turning trajectories of vehicles passing through multiple intersections. Each trajectory corres...
Solve probability and game-theory puzzles
You are interviewing for a quant trading internship. Answer the following probability / game-theory puzzles. 1) Two bottles, add/remove balls (100 rou...
Solve core probability and statistics questions
Answer the following short theory/computation questions (as in an OA multiple-choice section). Provide the key formula and a brief explanation. 1. Bay...
Solve Markov, OLS-rotation, and coin-toss probability
Answer the following three interview questions. 1) Basic properties of a Markov (transition) matrix Let \(P\) be a transition matrix of a (time-homoge...
How do you derive CDF from a PDF?
You are given a continuous random variable \(X\) with probability density function (PDF) \(f_X(x)\). 1. Write the definition of the cumulative distrib...
Plan for timed probability assessment
Timed Probability/Statistics Assessment Strategy (30 Questions, Strict Time Limit) Prompt You are taking a timed online assessment with 30 probability...
Estimate weather’s effect on mental health
Scenario You are studying whether weather (e.g., temperature, precipitation, sunlight, air pressure) affects mental health outcomes (e.g., depression ...
Solve estimation and probability brainteasers
Answer the following independent brainteaser questions. State any assumptions you need. 1) Tile a floor: A floor is 15 ft × 20 ft. You will cover it w...
Derive MLE and Bayesian posterior for Bernoulli
Bernoulli/Binomial Inference Task You observe n independent Bernoulli trials with unknown success probability p, and you record k successes (so K ~ Bi...
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...
Compute decay, OLS, and classic probability results
You are asked several probability/statistics questions. 1) Radioactive decay (half-life) A radioactive atom has a half-life of 1 day. Assume each atom...
Sketch distributions and compare mean/median/mode
Distribution sketches and summary-stat comparisons Answer the following conceptual statistics questions. Assume you have a large random sample and you...
Fake Accounts [AE]
Detecting and Managing Bad Accounts on a Social Platform 1) Probability of a Bad Account Sending Friend Requests Context: 1% of accounts are bad. Bad ...
Compute probabilities and expectations in random processes
You are asked to solve the following probability/expectation questions. Unless stated otherwise, assume all random choices are uniform and independent...
Compute robust inference under skew and outliers
A/B test with skew, outliers, heteroskedasticity, missingness, and multiplicity You are comparing two independent product variants that produce a cont...