Quantitative thinking on finance, data, and markets.https://atypicalquant.net/https://atypicalquant.net/blog/how-many-circles-will-you-create-in-your-bowl-of-ramen/https://atypicalquant.net/blog/how-many-circles-will-you-create-in-your-bowl-of-ramen/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…Mon, 27 Mar 2023 00:00:00 GMThttps://atypicalquant.net/blog/non-markovian-paper-tossing-challenge/https://atypicalquant.net/blog/non-markovian-paper-tossing-challenge/What is the probability of hitting a bin exactly 298 times out of 300 throws, when your hit rate equals your cumulative win rate? A clean induction proof.Mon, 20 Feb 2023 00:00:00 GMThttps://atypicalquant.net/blog/probabilities-and-moments/https://atypicalquant.net/blog/probabilities-and-moments/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…Mon, 16 Jan 2023 00:00:00 GMThttps://atypicalquant.net/blog/unfair-coin-detection/https://atypicalquant.net/blog/unfair-coin-detection/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…Mon, 19 Dec 2022 00:00:00 GMThttps://atypicalquant.net/blog/estimating-pi-quickly/https://atypicalquant.net/blog/estimating-pi-quickly/Write a code for estimating Pi up to 15 digits in under 1 second! Introduction Currently, the record for the best estimate of Pi approximates it with a…Mon, 14 Nov 2022 00:00:00 GMThttps://atypicalquant.net/blog/doubling-the-input-data-for-a-linear-regression/https://atypicalquant.net/blog/doubling-the-input-data-for-a-linear-regression/What happens if you duplicate the data used in OLS linear regression? You can encounter this problem in many forms; the one I first received was asking…Mon, 17 Oct 2022 00:00:00 GMThttps://atypicalquant.net/blog/unexpected-number-guessing-gamble/https://atypicalquant.net/blog/unexpected-number-guessing-gamble/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…Mon, 19 Sep 2022 00:00:00 GMThttps://atypicalquant.net/blog/summation-until-one/https://atypicalquant.net/blog/summation-until-one/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,…Mon, 22 Aug 2022 00:00:00 GMThttps://atypicalquant.net/blog/minimal-pairwise-correlation/https://atypicalquant.net/blog/minimal-pairwise-correlation/X, Y, and Z are three random variables with mutual pairwise correlation rho. What is the minimum possible value that rho can take? Definitions and…Mon, 25 Jul 2022 00:00:00 GMThttps://atypicalquant.net/blog/expectation-of-distances-on-a-disc/https://atypicalquant.net/blog/expectation-of-distances-on-a-disc/The expectation of distances on a disc: On a unit disc, what is the expected distance from a uniformly random point to its center? At a glance and letting…Mon, 27 Jun 2022 00:00:00 GMThttps://atypicalquant.net/blog/random-variable-comparison/https://atypicalquant.net/blog/random-variable-comparison/Solve the following random variable comparison: what is the probability that X > 4Y if : 1. X, Y independent, standard normally distributed? 2. X, Y…Mon, 30 May 2022 00:00:00 GMThttps://atypicalquant.net/blog/cards-to-draw-until-you-get-an-ace/https://atypicalquant.net/blog/cards-to-draw-until-you-get-an-ace/Drawing cards from a standard shuffled poker deck, how many cards do you expect to draw until you get an ace? Introduction: This question was asked by one…Mon, 02 May 2022 00:00:00 GMThttps://atypicalquant.net/blog/logarithm-inequality/https://atypicalquant.net/blog/logarithm-inequality/Solve the logarithm inequality: which is higher, log₂(3) + log₃(2) or 13/6? Two methods — bounding with powers of 2 and 3, and algebraic manipulation via a quadratic.Mon, 04 Apr 2022 00:00:00 GMThttps://atypicalquant.net/blog/100-people-in-line-to-board-a-plane/https://atypicalquant.net/blog/100-people-in-line-to-board-a-plane/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…Mon, 07 Feb 2022 00:00:00 GMThttps://atypicalquant.net/blog/more-heads-fewer-coin-tosses/https://atypicalquant.net/blog/more-heads-fewer-coin-tosses/Rick and Morty play a game where they flip 20 and 21 coins, respectively. What is the probability that Rick gets more heads? Introduction: As with most…Mon, 10 Jan 2022 00:00:00 GMThttps://atypicalquant.net/blog/number-guessing-game-quant-interview-questions/https://atypicalquant.net/blog/number-guessing-game-quant-interview-questions/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…Mon, 20 Dec 2021 00:00:00 GMThttps://atypicalquant.net/blog/cutting-a-cake-with-planes/https://atypicalquant.net/blog/cutting-a-cake-with-planes/By cutting a sphere with five planes, what is the maximum number of resulting chunks you can obtain? Introduction: Most of the time, with this type of…Mon, 22 Nov 2021 00:00:00 GMThttps://atypicalquant.net/blog/squid-game-surviving-round-5/https://atypicalquant.net/blog/squid-game-surviving-round-5/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…Tue, 02 Nov 2021 00:00:00 GMThttps://atypicalquant.net/blog/quant-interview-questions-efficient-majority-algorithm/https://atypicalquant.net/blog/quant-interview-questions-efficient-majority-algorithm/In a vector of length 2n, an element appears at least n+1 times. Find the most frequent element of the vector. Introduction: One obvious algorithm scans…Mon, 11 Oct 2021 00:00:00 GMThttps://atypicalquant.net/blog/tennis-tournament-winner-probabilities/https://atypicalquant.net/blog/tennis-tournament-winner-probabilities/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…Mon, 13 Sep 2021 00:00:00 GMThttps://atypicalquant.net/blog/quant-interview-questions-pirate-democracy/https://atypicalquant.net/blog/quant-interview-questions-pirate-democracy/A crew consisting of 3 democratic pirates finds a bounty of 100 coins. The strongest pirate must propose a bounty split and all pirates vote. If the vote…Sun, 01 Aug 2021 00:00:00 GMThttps://atypicalquant.net/blog/easiest-problem-from-imo-1985/https://atypicalquant.net/blog/easiest-problem-from-imo-1985/A circle has its center on the side AB of the cyclic quadrilateral ABCD. The other three sides are tangent to the circle. Prove that AD + BC = AB…Sun, 18 Jul 2021 00:00:00 GMThttps://atypicalquant.net/blog/quant-interview-questions-coupon-collectors-problem/https://atypicalquant.net/blog/quant-interview-questions-coupon-collectors-problem/A fair 6-sided die is rolled until you get every number on the die. The order in which the numbers appear does not matter. What is the expected number of…Sun, 04 Jul 2021 00:00:00 GMThttps://atypicalquant.net/blog/easiest-problem-from-imo-1984/https://atypicalquant.net/blog/easiest-problem-from-imo-1984/Prove that 0 ≤ yz + zx + xy − 2xyz ≤ 7/27, where x, y, z are positive real numbers with x + y + z = 1. A classic IMO 1984 inequality solved with AM-GM and Lagrange multipliers.Sun, 27 Jun 2021 00:00:00 GMThttps://atypicalquant.net/blog/consecutive-heads/https://atypicalquant.net/blog/consecutive-heads/A fair coin is tossed repeatedly until three consecutive tosses are heads. What is the expected number of coin tosses? Solution: Let x be the expected…Sat, 12 Jun 2021 00:00:00 GMThttps://atypicalquant.net/blog/grid-walking-problem/https://atypicalquant.net/blog/grid-walking-problem/A mouse starts at the bottom left corner of a [math]8 \times 6[/math] grid. At each step, he can only move RIGHT or UP, moving on the grid lines. He wants…Sun, 23 May 2021 00:00:00 GMThttps://atypicalquant.net/blog/south-park-alt-data-portfolio/https://atypicalquant.net/blog/south-park-alt-data-portfolio/Is a South Park Stock Market trading strategy viable? After the previous post, we gathered the data needed to construct our portfolio. First, we will have…Sat, 15 May 2021 00:00:00 GMThttps://atypicalquant.net/blog/trading-a-bouncy-stock/https://atypicalquant.net/blog/trading-a-bouncy-stock/For a given stock, you are certain that for the next 100 days, it will move either 10% up or 10% down each day. You can invest now, but if you choose to…Thu, 29 Apr 2021 00:00:00 GMThttps://atypicalquant.net/blog/expected-sum-of-distances/https://atypicalquant.net/blog/expected-sum-of-distances/In a triangle with sides 45, 60, respectively 75, what is the expected sum of distances from a point to its sides? Solution: Before we can actually find…Sat, 10 Apr 2021 00:00:00 GMThttps://atypicalquant.net/blog/renault-an-affordable-revolution/https://atypicalquant.net/blog/renault-an-affordable-revolution/Renault - Passion for Life 🟩 Company Outlook Headquartered near Paris, the Renault group is made up of the namesake Renault marque and subsidiaries:…Wed, 07 Apr 2021 00:00:00 GMThttps://atypicalquant.net/blog/getting-all-the-south-park-stock-market-references-by-scraping-wikipedia/https://atypicalquant.net/blog/getting-all-the-south-park-stock-market-references-by-scraping-wikipedia/Is a South Park Stock Market trading strategy viable? In the following, we will use Python to get a list of all the mentions of public companies mentioned…Mon, 29 Mar 2021 00:00:00 GMThttps://atypicalquant.net/blog/using-leverage-on-etoro/https://atypicalquant.net/blog/using-leverage-on-etoro/Things you need to consider when using leverage on eToro : Fees (aka the cost of capital/interest rate) While leverage fees vary from one stock to…Mon, 22 Mar 2021 00:00:00 GMThttps://atypicalquant.net/blog/why-im-bullish-on-orange/https://atypicalquant.net/blog/why-im-bullish-on-orange/Why is ORA.PA (Orange) my largest holding? 🟩 𝐂𝐨𝐦𝐩𝐚𝐧𝐲 𝐨𝐮𝐭𝐥𝐨𝐨𝐤 Operates in 27 countries, primarily providing telecom services, but recently…Mon, 22 Mar 2021 00:00:00 GMThttps://atypicalquant.net/blog/stock-merger-arbitrage-apha-tlry/https://atypicalquant.net/blog/stock-merger-arbitrage-apha-tlry/What is Stock Merger Arbitrage? What is Arbitrage? In economics, a strategy that takes advantage of a price difference between two or more markets is…Tue, 19 Jan 2021 00:00:00 GMT