Citadel Securities Interview Questions

Given 25 horses and a race track where only 5 horses can race at a time, what is the minimum number of races required to determine the fastest horse?

What is the square root of 800 rounded to two decimal places?

Write code to generate the Fibonacci sequence.

Given constraints on the correlations between three random variables, provide bounds for the correlation between one pair of them.

Describe a program to determine whether a given integer is a prime number.

What is the shape of the gamma curve for a call option?

What is the house edge of a standard game of roulette?

What is the probability that a coin is biased (always lands heads), given that you observe five heads in a row?

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?

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?

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?

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