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Mean and Variance of Discrete Uniform Distributions

Posted on May 3, 2021 Written by The Cthaeh 1 Comment

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.

[Read more…]

Filed Under: Algebra, Probability Distributions Tagged With: Discrete uniform distribution, Expected value, Mean, Variance

The Birthday Problem: Python Simulation

Posted on August 17, 2020 Written by The Cthaeh 6 Comments

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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Filed Under: Applications, Probability Theory & Statistics Tagged With: Discrete uniform distribution, Law of large numbers, Python

The Birthday Problem: Analytic Solution

Posted on August 11, 2020 Written by The Cthaeh 2 Comments

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

Welcome to the first post from my new series. Here we’re going look at a famous probability question often called the birthday problem. This is actually a more general question related to the probability of at least one coincidence after a fixed number of draws from a discrete uniform distribution.

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

[Read more…]

Filed Under: Applications, Combinatorics, Probability Theory & Statistics Tagged With: Discrete uniform distribution, Expected value, Permutation, Sample space

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Recent posts

  • Numeral Systems: Everything You Need to Know
  • Introduction to Number Theory: The Basic Concepts
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  • Mean and Variance of Discrete Uniform Distributions
  • Euclidean Division: Integer Division with Remainders

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