Citadel Data Scientist Statistics & Math Interview Questions
Master your tech interview with our curated database of real questions from top companies.
Derive Coefficient and Covariance in Regression Analysis
Correlation Structure, Regression Slopes, Covariance of Order Statistics, and Change-of-Variables You are given standard random variables and asked to...
Calculate Probability of Third Card Being an Ace
Probability Puzzle: Drawing Aces Setup - You draw 3 cards without replacement from a standard 52-card deck (4 Aces, 48 non-Aces). - It is known that a...
Derive distribution of an inverse transform
Change of Variables via the Logistic Map You are given a random variable X with density f_X supported on (0, 1). Define the strictly increasing logist...
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...
Compute P(third Ace | Ace in first two)
Conditional probability with cards drawn without replacement Problem You draw three cards without replacement from a standard 52‑card deck (4 Aces). G...
Solve probability and expectation problems
Probability and Statistics Mini-Set Context: Answer each item independently. Unless otherwise specified, assume independence and uniform randomness; d...
Compute variance of trading profits
Symmetric Random Walk Trading Strategy: Profit Variance and Expectation Setup - Let S_t be a simple symmetric random walk with S_0 = 0 and increments ...
Analyze profits under random walk and Brownian motion
Random-Walk Trading Rules: Expectation and Variance Setup - Let (S_t) be a simple random walk for t = 0, 1, ..., T with S_0 = 0. - Increments X_t = S_...
Explain multicollinearity and OLS assumptions
Linear Regression Technical Screen: OLS Assumptions and Multicollinearity Context: You are asked to summarize core OLS assumptions, explain multicolli...