Citadel Interview Questions

What is covariance?

Write a function to calculate Fibonacci numbers using recursion.

Suppose you roll two fair six-sided dice. What is the probability that the sum of the two dice is equal to 8?

How would you run a Monte Carlo simulation in Python to predict the probability of obtaining 4 out of 6 coins as heads, without using for loops?

What is the expected value of a fair six-sided die?

1. You have two fair dice. What is the probability that their sum is a prime number? 2. Three people play a game where each flips a coin. The last person with a different result wins. What is the expected number of flips? 3. What is 17 multiplied by 23? 4. What is the square root of 2907 to two decimal places? 5. If the S&P moves 0.3% and AAPL's beta is 1.2, what is AAPL's expected move? 6. Write a function to find arbitrage opportunities in a currency exchange matrix. 7. Given real-time trade data, design an algorithm to detect wash trading. 8. Implement a fast moving median calculator for streaming data. 9. How would you arbitrage S&P 500 futures versus the underlying basket? 10. What happens to options prices during earnings announcements? 11. Design a mean-reversion strategy for ETF pairs trading. 12. 100 people wear either red or blue hats. Each person can see others' hats but not their own. They must all simultaneously guess their own hat color. They can plan beforehand. How do they maximize group survival?

What are the assumptions of linear regression?

How would you design a machine learning algorithm that uses Twitter data to generate a trading strategy?

Write a Python function to calculate the variance of a given list of numbers.

How can you detect a loop in a linked list?