• Home
  • Announcements & Surveys
  • About
  • Contact

Probabilistic World

  • Probability Theory & Statistics
    • Fundamental Concepts
    • Measures
    • Probability Distributions
    • Bayes’ Theorem
  • General Math Topics
    • Number Theory
    • Algebra
    • Discrete Mathematics
      • Combinatorics
      • Cryptography & Cryptanalysis
  • Applications

Introduction to Probability Distributions

Posted on August 16, 2019 Written by The Cthaeh 7 Comments

A set of binomial distributions laid on top of a beach background

If you want to take your understanding of probabilities to the next level, it's crucial to be familiar with the concept of a probability distribution. In short, a probability distribution is an assignment of probabilities or probability … [Continue reading]

Filed Under: Probability Distributions Tagged With: Law of large numbers, Probability axioms, Probability density, Probability mass, Sample space

The Variance: Measuring Dispersion

Posted on December 8, 2018 Written by The Cthaeh 2 Comments

Small pawn-shaped magnets of different color, representing variance

A few posts ago I introduced you to the "three M's" of statistics — the concepts of mean, mode, and median. Today I want to talk to you about a related concept called variance. While the three M's measure the central tendency of a collection of … [Continue reading]

Filed Under: Fundamental Concepts, Measures Tagged With: Mean, Parameter estimation, Variance

Intuitive Explanation of Expected Value

Posted on November 24, 2018 Written by The Cthaeh 20 Comments

A pile of poker chips and a few dice

Expected value is another central concept in probability theory. It is a measure of the "long-term average" of a random variable (random process). I know this doesn't sound too clear, but in this post I'm going to explain exactly what it … [Continue reading]

Filed Under: Fundamental Concepts, Measures Tagged With: Coin flip, Expected value, Law of large numbers, Mean

The Law of Large Numbers: Intuitive Introduction

Posted on November 13, 2018 Written by The Cthaeh 17 Comments

The silhouette of an infinity symbol

The law of large numbers is one of the most important theorems in probability theory.  It states that, as a probabilistic process is repeated a large number of times, the relative frequencies of its possible outcomes will get closer and closer … [Continue reading]

Filed Under: Fundamental Concepts, Probability Theory & Statistics Tagged With: Coin flip, Law of large numbers

The Mean, the Mode, And the Median

Posted on October 1, 2018 Written by The Cthaeh 3 Comments

Mean, median, and mode of a distribution shown on a Spaghetti Western background

The concepts of mean, median, and mode are fundamental to statistics, probability theory, and anything related to data analysis as a whole. Being this important, they deserve their own introduction. In statistics, these 3 concepts are examples … [Continue reading]

Filed Under: Fundamental Concepts, Measures Tagged With: Mean, Parameter estimation

Occam’s Razor: A Probabilistic View

Posted on March 13, 2018 Written by The Cthaeh 7 Comments

The word simple written by blocks of "complex" words

"Simple explanations are better than complex explanations." — have you heard this statement before? It's the most simplified version of the principle called Occam's razor. More specifically, the principle says: A simple theory is always preferable to … [Continue reading]

Filed Under: Applications, Bayes' Theorem Tagged With: Causality

  • « Previous Page
  • 1
  • …
  • 3
  • 4
  • 5
  • 6
  • 7
  • 8
  • Next Page »

Sign Up For The Probabilistic World Newsletter

Enter your email below to receive updates and be notified about new posts.

Follow Probabilistic World

  • Facebook
  • Twitter
  • YouTube

Recent posts

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

Probabilistic World