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The Binomial Distribution (and Theorem): Intuitive Understanding

Posted on May 19, 2020 Written by The Cthaeh 5 Comments

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.

[Read more…]

Filed Under: Algebra, Combinatorics, Probability Distributions Tagged With: Bernoulli distribution, Binomial distribution, Coin flip, Mean, Probability mass, Variance

The Bernoulli Distribution: Intuitive Understanding

Posted on May 5, 2020 Written by The Cthaeh 1 Comment

A portrait of Jacob Bernoulli with a 17th century Swiss coin in the background

In today’s post, I’m going to give you intuition about the Bernoulli distribution. This is one of the simplest and yet most famous discrete probability distributions. Not only that, it is the basis of many other more complex distributions.

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

[Read more…]

Filed Under: Probability Distributions Tagged With: Bernoulli distribution, Coin flip, Law of large numbers, Mean, Probability mass, Variance

Discrete Probability Distributions: Overview (Series)

Posted on October 30, 2019 Written by The Cthaeh 4 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.

[Read more…]

Filed Under: Probability Distributions Tagged With: Coin flip, Probability mass, Sample space

Mean and Variance of Probability Distributions

Posted on August 28, 2019 Written by The Cthaeh 13 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.

[Read more…]

Filed Under: Probability Distributions Tagged With: Expected value, Law of large numbers, Mean, Probability density, Probability mass, Variance

Introduction to Probability Distributions

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

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 densities to all possible outcomes of a random variable.

For example, take the random process of flipping a regular coin. The outcome of each flip is a random variable with a probability distribution:

  • P(“Heads”) = 0.5
  • P(“Tails”) = 0.5

Depending on the type of random variable you’re working with, there are two general types of probability distributions: discrete and continuous. In this post, I’m going to give an overview of both kinds. And in follow-up posts I’m going to individually introduce specific frequently used probability distributions from each kind.

[Read more…]

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 varianceA 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 numbers, the variance measures their dispersion. That is, it measures how different the numbers are from each other.

Measuring dispersion is another fundamental topic in statistics and probability theory. On the one hand, it tells you how much you can trust the central tendency measures as good representatives of the collection. High variance usually means a lot of the numbers in the collection will be far away from those measures.

[Read more…]

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

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