quant interview

How Many Circles Will You Create in Your Bowl of Ramen?

atypicalquant
March 27, 2023January 5, 2024
11 Comments

There are 100 noodles in your bowl of ramen. You select two of their ends randomly and connect them, then put the resulting -maybe deformed- noodle back in the bowl. You repeat the process until there are no ends left to join. On average, how many circles will you create? For simplicity, provide the answer approximated to the closest integer.

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Non-Markovian Paper Toss Challenge: Aiming for 298 Wins

atypicalquant
February 20, 2023January 5, 2024

Let’s say you toss paper 300 times into a bin. You miss the first but nail the second one. Subsequently, your chance of hitting the bin is your cumulative win rate. What is the probability that you hit the can 298 times?

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Decoding Probabilities: The Minimum Value of P(X)=0

atypicalquant
January 16, 2023January 4, 2024
1 Comment

X is a random variable, taking positive integer values and having: E[X] = 1, E[X^2] = 2, and E[X^3] = 5. What is the smallest value that the probability of X equals 0 can take?

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Detecting Unfair Coins: How Many Flips Needed?

atypicalquant
December 19, 2022January 5, 2024

You receive a coin that is either fair (with a 50% probability of getting heads) or unfair (with a 42% probability). How can you detect the fair coin? And after how many flips can you assuredly say that?

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Fast Python Challenge: Estimating Pi to 15 Digits

atypicalquant
November 14, 2022January 4, 2024

Write a code for estimating Pi up to 15 digits in under 1 second!

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Doubling Data in OLS Linear Regression: Effects Explored

atypicalquant
October 17, 2022January 5, 2024

What happens if you duplicate the data used in OLS linear regression?

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Mastering the Number-Guessing Game: Strategies Beyond 50%

atypicalquant
September 19, 2022January 4, 2024

Two numbers are randomly chosen from the closed interval [0,1]. Afterward, you see the first number. You now must guess if the unseen number is greater or smaller.
Can you find a strategy with more than a 50% probability of winning?

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Expected Count in the ‘Sum Over One’ Game

atypicalquant
August 22, 2022January 4, 2024

You play a game where you sum independent identically distributed uniform random variables over the interval [0,1]. The first time the sum exceeds one, record the count of needed variables. What is the expected number of variables?

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Discovering the Minimum Pairwise Correlation: X, Y, Z

atypicalquant
July 25, 2022January 4, 2024

X, Y, and Z are three random variables with mutual pairwise correlation rho. What is the minimum possible value that rho can take?

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Calculating Expected Distance to Center on a Disc

atypicalquant
June 27, 2022January 4, 2024

The expectation of distances on a disc: On a unit disc, what is the expected distance from a uniformly random point to its center?

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