A small proof about multidimensional tic tac toe. Player 1 starts and plays crosses, player 2 places circles. The goal of the game is to get three crosses/circles in a row.
This repository contains different simulations of (mathematical) problems. You can find a description of these problems below:
The problem is defined as follows: Suppose we have a plane which is fully booked. The first person to enter is blind and therefore takes a random seat, if one of the passengers seats is already taken, they will take a random seat as well.
What is the probability that the last person to enter the plane will be able to sit in their assigned seat?
Exact answer: 0.5, this can be easily proven using induction.
Given a NxN grid, where the edges of each unit square are coloured either red or black (with p=0.5), what is the probability that none of the unit squares have all sides coloured the same:
Exact answer: [WILL BE ADDED ONCE SUBMISSIONS CLOSE]
This file is a study on how well it works if we take a sample of a dataset, after which we use this to create an empirical distribution and try to find the outliers of the data based on this. Which means that we do not have to iterate over the entire dataset. However, the results are quite poor, as can be seen in the result. Furthermore, we can not know for sure that the result of doing this multiple times converges.
An estimate of Pi by sampling points in the second quadrant of the unit square (using the fact that the estimated ratio of points in the second quadrant and in the unit circle wrt the previous one will be pi) uniformly.