Citadel–styleQuant Researcher InternQuant Research InternQuestion #125
Sample points randomly from a unit sphere. If you generate independent standard normal variables X1, X2, X3 for the three coordinates and normalize by dividing by sqrt(X1^2 + X2^2 + X3^2), then (X1, X2, X3) / sqrt(X1^2 + X2^2 + X3^2) is a uniform random point on the sphere. What is the variance of each coordinate of the resulting uniform distribution on the sphere?
Build Your Approach
State the assumptions, try a simple case, then work toward a general solution. Check the result and explain how it changes if an assumption changes.
Try the free diagnostic with worked solutions →Get Free Interview Prep Resources
More Citadel–Style Quant Researcher Intern Questions
If you have a dataset with many features, what methods can you use to reduce its dimensionality?How do you derive the Black-Scholes formula for pricing European options?1. Describe your past research experience related to reinforcement learning and model explainability. 2. Explain the bias-variance trade-off in random forests. 3. What is the closed-form solution to linear regression, with and without L2 regularization?Analyze the variance of a momentum trading strategy.Given the numbers 1 to 1000 arranged around a circle in order, start at 1 and delete every alternate number (i.e., remove 1, then 3, then 5, and so on). Continue this process of deleting every other remaining number, wrapping around the circle as necessary, until only one number remains. Determine this final remaining number.
Practice the Reasoning Behind the Answer
Bring your target roles and interview timeline to a free quant consult. Discuss your preparation priorities and how Quant Blueprint’s lessons, practice and mock interviews can help.
Book a Free Quant ConsultYour goals · your preparation · your next steps