Many introductory statistics courses include a considerable section on probability distributions, featuring the binomial and normal distributions. Consequently we have a suite of videos about probability distribution models, to help learners and teachers, especially those who wish to aim for conceptual more than mathematical understanding.

In this post I will outline the main videos available on the Dr Nic’s Maths and Stats YouTube Channel. They already belong to thousands of playlists and lists of recommended resources in textbooks the world over. We are happy for teachers and learners to continue to link to them. Having them listed here makes it easier for instructors to decide which ones to use in their courses.

You are welcome to link to our YouTube channel, and we get a tiny amount of money from advertising. Please encourage your students to subscribe to the channel and “like” the videos. If you have trouble with reliable internet access, you can purchase a licence for the videos along with files for your network. Do NOT download the videos, as it is against YouTube rules, and deprives us of income. See the end of the post for details.

This video explains what probability is and why we use it. It does NOT use dice, coins or balls in urns. There are other videos introducing basic probability (not distributions) with a conceptual approach. The other five videos can be accessed through subscription.

The idea of a random variable can be surprisingly difficult. In this video we help you learn what a random variable is, and the difference between discrete and continuous random variables. It uses the example of Luke and his ice cream stand. There is a little exercise to identify discrete and continuous random variables.

This video uses the example of Luke’s ice cream stand, modelling the number of ice creams purchased. It has quite a few formulas in it. It shows how to calculate the expected value and standard deviation of a discrete random variable. It illustrates the rules for combining discrete distributions and multiplying by a scale factor. In each case it gives an example and shows the effect using simulation on Excel.

Again Luke’s ice cream stand features in the video, giving a cohesive context. Many students struggle with the idea of a probability distribution. This video emphasises that a distribution is a model that can be used to approximate a real-world situation. It is unusual in that it provides three competing models for the same data, involving weights of ice creams. The triangular distribution, which is part of the curriculum in New Zealand schools, is provided as an alternative for the normal distribution. You can read more about the value of teaching the triangular distribution here: Let’s hear it for the Triangular Distribution.

The Binomial distribution is often used as an introduction to probability distributions. This video again uses the example of Luke’s ice cream stand, with ice cream cones that break, to show the nature of a binomial distribution. It uses an online app for finding the probability values, and the formula is neither derived nor applied. You can find the app here: Binomial Calculator

In this video we explain the characteristics of the normal distribution, and why it is so useful as a model for real-life entities. In the second part of the video, it combines multiple small discrete distributions, showing how they iterate towards a normal distribution. All examples are done using simulation on Excel. The third part of the video illustrates why you need to find the area under the graph to find the probability for a range of values in a continuous distribution. One difficult concept is that for a continuous distribution, the probability of an exact value of the random variable is zero. This video shows why this is the case, and how it applies in practical terms.

This video provides a transition from the mathematical world of probability distributions to the use of distributions in statistical inference. The video uses the example of taking samples of different sizes and showing how the sampling distribution of the mean is well-modelled by the normal distribution.

As explained in a previous post, Lessons for a budding Social Enterprise, Creative Maths, including Statistics Learning Centre is a social enterprise, with our aim to build a world of mathematicians and enable people to make intelligent use of statistics. Though we get some income from YouTube videos, it does not support the development of more videos. If you would like to help us to create further videos contact us to discuss subscriptions, sponsorship, donations and advertising possibilities. info@CreativeMaths.net or n.petty@CreativeMaths.net.