Probabilistic World

Negative Numbers and Arithmetic: Intuition

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Many numbers of different sizes with the planet Earth in the background and the text "negative numbers" in the foreground

Hi everyone, and welcome to the next post from our journey in the world of numbers. Where we last left off, I was telling you about natural numbers — the objects that most naturally appear when we make our first steps in the world of Mathematics. Well, today’s post is about the next most natural kind of mathematical objects: negative numbers and the new structure they form together with natural numbers called integers!

This post is part of my series Numbers, Arithmetic, and the Physical World.

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The Future of Probabilistic World (Announcement & Survey)

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A map of a mysterious probabilistic world

Would you like to upgrade your probability theory, statistics, and math skills and bring them to the next level? Take a few minutes to answer today’s 7-question survey! I want to learn about your specific interests, both in mathematics and other areas in life where we can apply the ideas explored in the theoretical posts.

This is the first of many small surveys with which I want to give you, the readers, an opportunity to play a bigger role in the choice of topics to be covered.

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Alternative Variance Formulas and Their Derivation

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The equations of three alternative variance formulas

In today’s post I want to show you two alternative variance formulas to the main formula you’re used to seeing (both on this website and in other introductory texts).

Not only do these alternative formulas come in handy for the derivation of certain proofs and identities involving variance, they also further enrich our intuitive understanding of variance as a measure of dispersion for a finite population or a probability distribution.

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The Sum Operator: Everything You Need to Know

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The sum operator (capital Greek letter Sigma), light beams in the background

I have used the sum operator in many of my previous posts and I’m going to use it even more in the future. I’ve introduced bits and pieces about this notation and some of its properties but this information is scattered across many posts. For these reasons, I decided to dedicate a special post to the sum operator where I show you the most important details about it.

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Natural Numbers and Arithmetic: Intuition

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Many numbers of different sizes with the planet Earth in the background and the text "natural numbers" in the foreground

Welcome to the third post from my series on numbers and arithmetic. In the previous two posts, I gave an overview of real numbers (and their main subsets), as well as the main operations between them. And in the rest of the series, we’re going to build all these concepts from scratch. Well, the focus in today’s post is the most basic subset of the real numbers: the natural numbers.

This post is part of my series Numbers, Arithmetic, and the Physical World.

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The Birthday Problem: Python Simulation

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UEFA Nations League semi-final between Netherlands and England (prematch, 06/06/2019), with Python code related to the birthday problem in the background

In my last post, I introduced you to the so-called birthday problem. Namely, the probability of having at least one birthday coincidence in a random group of people. I showed you how to approach the question analytically by deriving a simple formula for calculating this probability.

In this post, I want to show you an alternative way of getting the same probability using a computer simulation with the programming language Python!

This post is part of my series Probability Questions from the Real World.

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