Probabilistic World

Mean and Variance of Discrete Uniform Distributions

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A crowd of white Lego figures

In today’s (relatively) short post, I want to show you the formal proofs for the mean and variance of discrete uniform distributions. I already talked about this distribution in my introductory post for the series on discrete probability distributions. Well, this is a pretty simple type of distribution that doesn’t really need its own post, so I decided to make a post that specifically focuses on these proofs. More than anything, this is going to be a small exercise in algebra.

This post is part of my series on discrete probability distributions.

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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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What are Mathematical Functions?

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Wheat (x) turning to flour and dough (f(x)) - metaphorically representing the argument of a function and the function itself

The topic of today’s post is mathematical functions. Functions are such a fundamental part of mathematics that you’re certain to encounter them almost everywhere.

Recently, I started a small series on numbers and arithmetic, in order to begin exploring the intuition of basic mathematical concepts that most of us take for granted. And these concepts themselves are the building blocks of more advanced concepts, including more advanced concepts in probability theory.

But to fully understand them, we also need to know the details and intuition of some general mathematical tools which we’re going to rely on along the way. Well, functions are first in line!

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The Binomial Distribution (and Theorem): Intuitive Understanding

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A skyscraper resembling a binomial distribution

Hi, everyone! And welcome to my post about the binomial distribution! Just like the Bernoulli distribution, this is one of the most commonly used and important discrete probability distributions.

This post is part of my series on discrete probability distributions.

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