Citadel Interview Questions

How will the probability of an option ending up in the money change if the volatility of the underlying stock increases?

What is the difference between Gaussian Naive Bayes (GNB) and logistic regression? Under what circumstances would you choose one over the other?

Given that log X is normally distributed with mean 0 and variance 1, compute the expected value of X.

How do you estimate the square root of 5?

You have two strings, each of which takes exactly one hour to burn completely when lit at one end. The rate of burning is non-uniform and differs between the strings. Using only these two strings and a way to light them, how can you measure 45 minutes?

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?

Write a function to traverse a binary tree without using recursion.

How would you construct an options position that is long vega and short gamma?

What is the probability of finding two consecutive ones in a randomly generated binary string of length n, where each bit is equally likely to be 0 or 1?

What is the probability of picking two diamonds and one card that is not a diamond from a standard deck of 52 cards?

Suppose I have two pancakes: one with both sides burnt, and one with one burnt side and one unburnt side. I randomly choose one pancake, then randomly look at one of its sides. If the side is burnt, what is the probability that I picked the pancake with both sides burnt?

What is the probability of getting a three-of-a-kind in Texas Hold'em poker?

Implement a class for the game Connect 4.

Given an array v, find the number of pairs of indices (i, j) such that v[i] = v[j] = v[i+1] + v[i+2] + ... + v[j-1]. Your solution should have time complexity O(n log n).

How would you solve a scheduling issue given a directed acyclic graph (DAG) of tasks and k computers? What if k is one or infinity?

Design an algorithm to randomly select people in a city such that the probability of selecting someone from a given district is proportional to the district's population size. Additionally, discuss how you would test your implementation and optimize its runtime, considering repeated calls to the selection function with an acceptable error margin.

If a Binary Search Tree was implemented incorrectly such that a node has a left child that is not smaller than itself, how would you detect this violation? What is the most efficient method to identify this issue?

There are three random variables, X, Y, and Z. The three correlations between the variables are equal, i.e., ρ = Corr(X, Y) = Corr(Y, Z) = Corr(Z, X). What is the tightest possible bound you can give for ρ? How about the general case for n random variables?

What is the difference between LASSO and ridge regression?

Describe linear regression in detail.

Given an n x n chessboard, return the minimum number of knight moves required to get from point (a, b) to point (c, d).

Return a minimum-length list of perfect squares whose sum equals a given value k.