Citadel Securities Interview Questions

Write Python code to determine if a given integer is a prime number.

Arrange the numbers 1 through 5 randomly around a circle. What is the expected number of numbers that are smaller than both of their neighbors?

What is the expected number of rolls needed to see each side of a fair six-sided die at least once?

If you find a coin on the street, what is the probability that it is a biased (unfair) coin?

Price an option where the underlying asset is the outcome of a fair six-sided die roll.

Two tennis players, A and B, are at deuce. Player A wins a point with a 60% chance, and Player B wins a point with a 40% chance. What is the probability that A wins the game?

You and a friend each independently receive a value drawn uniformly from (0,1). After seeing your value, you can choose to switch values with your friend or keep your original value. What is the probability that you end up with a higher value than your friend at the end of the game?

James goes to the gym every Monday and Tuesday. On every other day of the week, he independently has a 30% chance of going to the gym. On a random day, James is spotted at the gym. What is the probability that it is Monday?

Coin A lands heads with probability 2/3, and coin B lands heads with probability 1/3. If you flip the selected coin three times and observe heads each time, what is the probability that the coin is coin A?

If N people each put their hat in a room and then each randomly pick one hat, what is the probability that a given person gets their own hat back?

Derive and explain the concept of put-call parity in options pricing.

Given n random variables from the same distribution, where the correlation between each pair of two variables is the same, what is the range of possible values for the correlation?

Coin A shows heads with probability 2/3, and coin B shows heads with probability 1/3. If a coin is chosen at random and flipped three times, each resulting in heads, what is the probability that the coin is coin A?

How can you implement a rolling mean and variance of a data stream in O(1) time per update?

What is the expected value of the maximum among N normally distributed random variables?

Given a number, determine whether it can be represented as the sum of two or more consecutive integers.

What is the expected number of rolls of a fair six-sided die required until each face has appeared at least twice?

Implement a ring buffer data structure. Write functions for both writing data to the buffer and reading data from it.

How do you implement a rolling mean and variance for a data stream in O(1) time per update?

What is the expected value of the maximum of N independent normally distributed variables?

Three random variables X, Y, and Z are such that corr(X, Y) = corr(Y, Z) = corr(Z, X) = r. Give the upper and lower bounds for r.

What is the expected value of a fair 6-sided die?

If you flip 8 fair coins, what is the probability that more than 4 of them are heads?

Estimate how many basketballs can fit in a standard school bus.

How is std::map implemented internally?

You have a scale and 18 balls. One of the balls is slightly heavier than the rest, which are identical. What is the minimum number of times you need to use the scale to determine which ball is the heavy ball?

Implement a service to maximize throughput by increasing the number of processes, given a fixed budget constraint.