Two Sigma·Software Engineer·Technical Phone Screen
Jun 2026
Two Sigma quant-style interview covering probability, linear algebra, and econometrics. The problems were layered, each part building on the last, and the regression bias derivation at the end was where things got real.
- Given three zero-mean, unit-variance random variables with equal pairwise correlation p, what is the valid range of p?
- Construct an explicit example of three such variables that achieves any valid p in that range.
- Generalize the equal-correlation setup to n variables. What is the admissible range of p now?
- In a linear regression where the true model includes regressors X and Z but you only regress y on X, derive the OLS estimator you get and characterize the omitted variable bias in matrix form.
“You need the joint covariance matrix to be positive semi-definite, so the determinant constraint gives you p >= -1/2.” The rest of the author's notes on Software Engineer interview at Two Sigma, Technical Phone Screen round, covers how they worked through the question, what the panel pushed back on, and what they would do differently.
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