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Discrete Probability Distributions: An Overview

Posted on October 30, 2019 Written by The Cthaeh 2 Comments

A discrete probability distribution, two hands holding dice, and a background referencing the movie The Matrix

In my previous two posts I sketched the frame of the big picture around probability distributions. In my introductory post I gave some intuition about the general concept and talked about the two major kinds: discrete and continuous distributions. And in the follow-up post I related the concepts of mean and variance to probability distributions. I showed that this connection itself goes through two fundamental concepts from probability theory: the law of large numbers and expected value.

Now I want to build on all these posts. My plan is to start introducing commonly used discrete and continuous distributions in separate posts dedicated to each one. And I want to start with the former, since they are significantly easier to understand.

The goal of the current post is to be a final warm-up before delving into the details of specific distributions.

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Filed Under: Probability Theory Tagged With: discrete probability distribution, probability distribution

Mean And Variance Of Probability Distributions

Posted on August 28, 2019 Written by The Cthaeh 2 Comments

In my previous post I introduced you to probability distributions.

In short, a probability distribution is simply taking the whole probability mass of a random variable and distributing it across its possible outcomes. Since every random variable has a total probability mass equal to 1, this just means splitting the number 1 into parts and assigning each part to some element of the variable’s sample space (informally speaking).

In this post I want to dig a little deeper into probability distributions and explore some of their properties. Namely, I want to talk about the measures of central tendency (the mean) and dispersion (the variance) of a probability distribution.

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Filed Under: Probability Theory Tagged With: expected value, law of large numbers, mean, probability distribution, variance

Introduction To Probability Distributions

Posted on August 16, 2019 Written by The Cthaeh 3 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 Theory Tagged With: law of large numbers, probability density, probability distribution

The Variance: Measuring Dispersion

Posted on December 8, 2018 Written by The Cthaeh Leave a Comment

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: Probability Theory Tagged With: mean, parameter estimation, variance

An Intuitive Explanation Of Expected Value

Posted on November 24, 2018 Written by The Cthaeh 5 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: Probability Theory Tagged With: expected value, law of large numbers, mean

The Law Of Large Numbers: Intuitive Introduction

Posted on November 13, 2018 Written by The Cthaeh 9 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 to … [Continue reading]

Filed Under: Probability Theory Tagged With: law of large numbers

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Recent posts

  • Discrete Probability Distributions: An Overview
  • Mean And Variance Of Probability Distributions
  • Introduction To Probability Distributions
  • The Variance: Measuring Dispersion
  • An Intuitive Explanation Of Expected Value

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