QR Statistics / Domain Knowledge Oral

Math-heavy oral round covering statistics, regression, Markov chains, random graph expectations, and candidate-specific domain knowledge. The interviewer expects derivations, not just concept names. Requirements Prepare for verbal and whiteboard-style derivations across statistics and domain topics. Reported prompts include: Markov-chain question where an approximation was rejected and an analytic solution was requested, leading to a cubic equation. Pairwise correlation matrix feasibility: range of correlation p for variables x, y, z, determinant / eigenvalue / cosine-theta reasoning, and extension to n variables. Covariance of the maximum and minimum of n i.i.d. Uniform(0, 1) variables using E[XY] - E[X]E[Y] and a joint distribution integral. Omitted-variable bias in regression, including the impact on beta and a matrix-form proof. Complete graph with random continuous edge weights: a pair (a, b) is good if each endpoint is the other's maximum-weight neighbor; compute the expected number of good pairs. Resume / research-domain deep dive when the interviewer shares the candidate's background. Notes This round can be labeled statistics, domain knowledge, or core statistics depending on the loop. The strongest answers write down distributions, constraints, and formulas early. Hand-wavy ML intuition is not enough. If a closed form is requested, do not stop at simulation or approximation unless the interviewer accepts it. Preparation Review linear algebra conditions for valid correlation matrices: positive semidefinite constraints, eigenvalues, and determinant checks. Derive order-statistic joint distributions for min/max of uniform variables. Practice omitted-variable bias in scalar and matrix notation. Solve small expected-value graph problems using indicator variables and linearity of expectation.