Point72 Quantitative Research Intern Interview Experience — A Broad Second Round Covering Probability, Stats, ML, and LeetCode

Recruitment process: five rounds of interviews in total. This is the second round.

Behavioral

• Self-introduction
• How I taught myself finance knowledge

Technical

Probability

Question 1: The classic three-roll dice expectation problem. You can roll a die up to three times, and after each roll you can choose to stop. Your final payoff is the value of the last roll. Compute the expected value of the game. (This is the classic Optimal Stopping Problem.)

Question 2: Probability that two people meet. Both people arrive at a random time within one hour (uniform distribution), and each will wait at most 15 minutes. What's the probability they meet?

Solution: A classic geometric probability problem. Draw a 1x1 square where the x-axis is A's arrival time and the y-axis is B's arrival time. The condition |A - B| <= 15 min corresponds to a band-shaped region through the middle of the square. Use the area ratio to get the answer.

Question 3: Poisson Process. On a given road, the probability of at least one car showing up within an hour is 0.96. What's the probability of at least one car showing up within half an hour?

Solution: First compute the complement — probability of no car in an hour: P = 0.04. Using independent increments (Poisson process), let p be the probability of no car in half an hour. Then p^2 = 0.04, so p = 0.2. Therefore the probability of at least one car in half an hour is 1 - 0.2 = 0.8.

Statistics

Mostly basic statistics concepts, including: p-value, significance level (alpha), Type I Error, Type II Error, Null Hypothesis, Alternative Hypothesis, and various hypothesis tests — Z-test, t-test, Chi-square Test, F-test.

Machine Learning

Mostly conceptual questions, for example: What is Ensemble Learning? What are common ensemble methods? They didn't go deep into model derivations.

Coding (C++)

Asked some basic object-oriented concepts, including Encapsulation, Inheritance, and Polymorphism. Fairly basic C++ OOP knowledge.

Algorithm

Question 1: Best Time to Buy and Sell Stock II. Given an array of stock prices, you can trade an unlimited number of times, but can hold at most one share at a time. What's the maximum profit?

Solution: Greedy. Whenever today's price is higher than yesterday's, capture the full increase. One pass through the array is enough. Time Complexity: O(N). Space Complexity: O(1).

Question 2: Rotated Sorted Array. Given a sorted array that's been rotated k times, e.g. 4 5 6 7 0 1 2, how do you find the minimum value (the original starting point before rotation)?

Solution: Binary Search. Each time, compare the left and right halves to figure out which one is still increasing, and only keep searching the half that contains the rotation point. Eventually you find the minimum value. Time Complexity: O(log N). Space Complexity: O(1).

Overall impression

This round covered a lot of ground — beyond probability and statistics, it also tested basic quant research thinking, probability, statistics, basic machine learning concepts, C++ object-oriented programming, and common LeetCode-style algorithm questions. Overall the difficulty was fairly basic, with no particularly tricky math derivations — it was more about breadth of knowledge and whether the fundamentals are solid.