quant interview

Probability Analysis: Comparing X to 4Y in Random Variables

atypicalquant
May 30, 2022January 4, 2024

Solve the following random variable comparison: what is the probability that X > 4Y if :

1. X, Y independent, standard normally distributed?

2. X, Y independent, uniformly distributed on [0,1]?

Drawing Cards for an Ace: Calculating Expectations

atypicalquant
May 2, 2022January 4, 2024

Drawing cards from a standard shuffled poker deck, how many cards do you expect to draw until you get an ace?

Solving a Logarithm Inequality: Log vs Fraction

atypicalquant
April 4, 2022January 4, 2024

Solve the following logarithm inequality: which number is higher: $log_2(3) + log_3(2)$ or $\frac{13}{6}$ ?

Plane Boarding Puzzle: Will the Last Person Get Their Seat?

atypicalquant
February 7, 2022January 4, 2024

There are 100 people in line to board a plane that seats all of them. The first person in line is drunk and decides to take a random seat. Every person that boards the plane after them will either: take the seat on their ticket or if that seat is taken, a random one instead.

What is the probability that the last person that boards will end up in their assigned seat?

Coin Flip Game: Can You Win with Fewer Tosses?

atypicalquant
January 10, 2022January 4, 2024

Rick and Morty play a game where they flip 20 and 21 coins, respectively. What is the probability that Rick gets more heads?

Optimal Strategy in a Number Guessing Game

atypicalquant
December 20, 2021January 4, 2024
1 Comment

You play a number guessing game in which you must pick a real number x, between 0 and 924. At the same time, the number y is uniformly and randomly selected from the same range. If x is greater than y, then you have to pay the square of the difference between the two numbers. If y is greater than or equal to x, you pay double the difference.

What number should you choose initially?

Max Chunks from 5 Cuts in a Sphere: Solving the Puzzle

atypicalquant
November 22, 2021January 4, 2024

By cutting a sphere with five planes, what is the maximum number of resulting chunks you can obtain?

Squid Game Bridge: Calculating Survival Odds

atypicalquant
November 2, 2021January 4, 2024

Ahead of the players is the Squid Game Bridge with 18 steps, each made of a pair of glass tiles: one of them can hold the weight of a player, while the other can’t.

Players advance on the bridge in a predetermined order, one pair of tiles at a time.

If they choose a solid tile, they advance, otherwise, they are eliminated.

What is the expected number of survivors in a 16-player game?

Find the Guaranteed Majority Element in a Vector

atypicalquant
October 11, 2021January 4, 2024

In a vector of length 2n, an element appears at least n+1 times. Find the most frequent element of the vector.

Calculating Odds for Third Player’s Tennis Win

atypicalquant
September 13, 2021January 4, 2024

quant interview

Probability Analysis: Comparing X to 4Y in Random Variables

Solve the following random variable comparison: what is the probability that X > 4Y if :

1. X, Y independent, standard normally distributed?

2. X, Y independent, uniformly distributed on [0,1]?

Drawing Cards for an Ace: Calculating Expectations

Drawing cards from a standard shuffled poker deck, how many cards do you expect to draw until you get an ace?

Solving a Logarithm Inequality: Log vs Fraction

Solve the following logarithm inequality: which number is higher: $log_2(3) + log_3(2)$ or $\frac{13}{6}$ ?

Plane Boarding Puzzle: Will the Last Person Get Their Seat?

There are 100 people in line to board a plane that seats all of them. The first person in line is drunk and decides to take a random seat. Every person that boards the plane after them will either: take the seat on their ticket or if that seat is taken, a random one instead.

What is the probability that the last person that boards will end up in their assigned seat?

Coin Flip Game: Can You Win with Fewer Tosses?

Rick and Morty play a game where they flip 20 and 21 coins, respectively. What is the probability that Rick gets more heads?

Optimal Strategy in a Number Guessing Game

What number should you choose initially?

Max Chunks from 5 Cuts in a Sphere: Solving the Puzzle

By cutting a sphere with five planes, what is the maximum number of resulting chunks you can obtain?

Squid Game Bridge: Calculating Survival Odds

Ahead of the players is the Squid Game Bridge with 18 steps, each made of a pair of glass tiles: one of them can hold the weight of a player, while the other can’t.

Players advance on the bridge in a predetermined order, one pair of tiles at a time.

If they choose a solid tile, they advance, otherwise, they are eliminated.

What is the expected number of survivors in a 16-player game?

Find the Guaranteed Majority Element in a Vector

In a vector of length 2n, an element appears at least n+1 times. Find the most frequent element of the vector.

Calculating Odds for Third Player’s Tennis Win

Three equally skilled tennis players play in a tournament.

After each round, the winner plays against the third player.

The first to reach two consecutive wins becomes the champion.

If A and B play the first game, what is the probability that C is the tennis tournament winner?

quant interview

Solve the following random variable comparison: what is the probability that X > 4Y if :

1. X, Y independent, standard normally distributed?

2. X, Y independent, uniformly distributed on [0,1]?

Drawing cards from a standard shuffled poker deck, how many cards do you expect to draw until you get an ace?

Solve the following logarithm inequality: which number is higher: or ?

There are 100 people in line to board a plane that seats all of them. The first person in line is drunk and decides to take a random seat. Every person that boards the plane after them will either: take the seat on their ticket or if that seat is taken, a random one instead.

What is the probability that the last person that boards will end up in their assigned seat?

Rick and Morty play a game where they flip 20 and 21 coins, respectively. What is the probability that Rick gets more heads?

What number should you choose initially?

By cutting a sphere with five planes, what is the maximum number of resulting chunks you can obtain?

Ahead of the players is the Squid Game Bridge with 18 steps, each made of a pair of glass tiles: one of them can hold the weight of a player, while the other can’t.

Players advance on the bridge in a predetermined order, one pair of tiles at a time.

If they choose a solid tile, they advance, otherwise, they are eliminated.

What is the expected number of survivors in a 16-player game?

In a vector of length 2n, an element appears at least n+1 times. Find the most frequent element of the vector.

Three equally skilled tennis players play in a tournament.

After each round, the winner plays against the third player.

The first to reach two consecutive wins becomes the champion.

If A and B play the first game, what is the probability that C is the tennis tournament winner?

Solve the following logarithm inequality: which number is higher: $log_2(3) + log_3(2)$ or $\frac{13}{6}$ ?