Compute Gaussian Probability and Regression Coefficients
Company: Point72
Role: Machine Learning Engineer
Category: Machine Learning
Difficulty: medium
Interview Round: Technical Screen
You are given two independent standard normal random variables, X and Y.
1. Compute P[X > 3Y].
2. In ordinary linear regression with design matrix X in R^{n x p}, response vector y in R^n, and coefficient vector beta in R^p, how do we estimate beta?
3. If n is much larger than p, how can beta be computed efficiently and exactly?
Overview: This question evaluates probabilistic reasoning with Gaussian variables and parameter estimation in ordinary least squares regression, covering deriving probabilities for linear combinations of standard normals and computing regression coefficients via linear algebra.