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Alternative Variance Formulas and Their Derivation

Posted on November 15, 2020 Written by The Cthaeh Leave a Comment

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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Filed Under: Probability Distributions, Statistics Tagged With: Arithmetic, Expected value, Mean, Variance

The Sum Operator: Everything You Need to Know

Posted on November 2, 2020 Written by The Cthaeh Leave a Comment

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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Filed Under: General Mathematical Concepts Tagged With: Arithmetic, Function

Natural Numbers and Arithmetic: Intuition

Posted on October 7, 2020 Written by The Cthaeh Leave a Comment

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 … [Continue reading]

Filed Under: General Mathematical Concepts Tagged With: Arithmetic, Number

The Birthday Problem: Python Simulation

Posted on August 17, 2020 Written by The Cthaeh 4 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 … [Continue reading]

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

The Birthday Problem: Analytic Solution

Posted on August 11, 2020 Written by The Cthaeh Leave a Comment

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 … [Continue reading]

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

Probability Questions from the Real World (With Simulations)

Posted on August 2, 2020 Written by The Cthaeh Leave a Comment

A cartoon comically illustrating probability questions, taken from Henk Tijms' book "Understanding Probability: Chance Rules in Everyday Life"

Welcome to my introductory post to a large series that I'm starting today. The main purpose of this post is to get you in the mood for the posts to follow. Namely, exploring and solving interesting probability questions from the real world. … [Continue reading]

Filed Under: Applications of Probability Theory Tagged With: Python

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Recent posts

  • Alternative Variance Formulas and Their Derivation
  • The Sum Operator: Everything You Need to Know
  • Natural Numbers and Arithmetic: Intuition
  • The Birthday Problem: Python Simulation
  • The Birthday Problem: Analytic Solution

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