Math & Statistics interview questions

How would you compute (XᵀX)⁻¹XᵀY with limited RAM? Minimize the number of disk-to-RAM transfers.

What anomaly detection methods do you know? How would you identify anomalies in ship delay data?

How does an empirical cumulative distribution function (CDF) differ from a density histogram (PDF)?

A and B are arrays sampled from a uniform distribution on [0, 1023]. For each b, an a is selected to maximize their XOR. What is the distribution of the result? What changes for [0, 999]?

Why is the analytical OLS solution (X^T X)^{-1} X^T y generally not used in practice for linear regression?

When the data contains outliers, is it better to optimize MAE or MSE? Why is MSE commonly used?

How would you determine the required duration of an A/B test?

How would you estimate market impact from order execution data?

How would you run an A/B test of two execution algorithms in live trading?

Describe your experience with A/B testing.

What is an A/A test, and why is it needed?

In an A/B test, 5 out of 100 metrics show a statistically significant positive result, while the rest are neutral. Should we roll out the change?

Explain the difference between covariance and correlation. When can Pearson correlation be zero despite a dependency?

What is a p-value? Does p-value = 0.03 mean there's a 3% chance the null hypothesis is true?

Explain the Central Limit Theorem and why it's important for A/B testing.

How to calculate sample size for an A/B test? What parameters are needed and how do they affect n?

What is bootstrap? How to construct confidence intervals with it? When is bootstrap better than analytical formulas?

Bayesian vs frequentist A/B testing: what's the difference and when to choose Bayesian?

A/B test: control conversion 10%, want to detect 0.5% absolute lift. Day 3 p-value = 0.03. Should you stop?

Explain Simpson's paradox with an ML/analytics example where ignoring a confounder leads to wrong conclusions.