GSA Capital Quant Research Internship Second Round Tech Phone Screen

Back-to-back interviews, and I failed as expected. The first interviewer was a white-haired man. He asked the Monte Carlo problem: given two distributions, what algorithm is best to estimate P(X<Y)? I

Back-to-back interviews, and I failed as expected. The first interviewer was a white-haired man. He asked the Monte Carlo problem: given two distributions, what algorithm is best to estimate P(X3X| X>0, Y>0), which also seemed to be a green-skinned question. I was grilled about why the area was calculated as a disk instead of a square, which I didn't answer well. Then the interviewer gave an example related to the distribution: X,Y~U([0,1]) would be a square. It took me a while to answer that X^2 + Y^2 ~ exp(1/2) is independent of x and y. Finally, for the LeetCode coin toss question, I answered instantly, but it wasn't bug-free. I pointed out a problem and fixed it, and it

passed. The follow-up was proving that O(n+k) time was insufficient. After thinking for a moment, I drew him a tree and said that if you were counting the number of paths, linear time wouldn't be feasible. He said it was acceptable, but the actual proof might be more rigorous. During the Q&A session, since I felt I should have already submitted my answer, I thought I'd chat with him a bit, having some lighthearted small talk. Then, at some point, he said "see you next time" and immediately hung up. I felt it was right to waste his time on someone like that.