This is one of my favourites: in 1840 the German mathematician Dirichlet proved an elegant theorem, known as “Dirichlet’s approximation theorem“. The proof is surprisingly simple, but the usefulness of the proposition in some fields of mathematics, such as Diophantine analysis is remarkable. It goes as follows: Let a be ... [Read more...]

I have been using R for about two years, with no previous coding background. So, I feel like the title says, “always learn and never know”. This time, I decided to use R to study a simple, non-statistical problem that came up some time ago. Suppose the exponential function 2^x ... [Read more...]

Suppose the following game with two players: In every round, the two players pick a random number, each. Instead of using a dice, they pick a number from an interval. Player A picks a number from [9,11] and player B from [8,12]. Variation 1. The greater number wins. Who is more likely to ... [Read more...]

Today we will use R to extract some interesting summary statistics regarding the music files stored in the computer. For all mp3 files I keep certain metadata in their ID3 tag. We will use this information to explore the distribution of music files with respect to the year of release. ... [Read more...]

In a previous post I introduced the following game: Suppose you play the following game: Someone holds a set of cards with the numbers {1,2,…,N} in random order, opens up the first card and asks if the next card is greater or smaller. Every time you predict correctly, you get ... [Read more...]