Peer Review

The idea for Probability Playground came about while I was taking the Biostatistics MA program at the University at Buffalo. Classes in probability theory and statistics referred to over a dozen common probability distributions, their mass or density functions, their moments, and how to derive them. By the end of the first year I could work with these distributions algebraically, but still didn't have a intuitive feel for many of them. I was often left with the following unanswered questions: What kinds of shapes can the graphs of the distributions take, and how do these shapes depend on the parameters? How do the distributions arise naturally? If one distribution converges to another distribution, under what circumstances is it a good approximation? If one distribution is a special case of another, how do the shapes of their probability mass or density functions compare? If one distribution is a transformation of another, how does it change as the shape of the other distribution changes? If one distribution is derived from a sample of another distribution, how does its shape change as the sample size increases? Probability Playground was designed as an interactive tool for answering these questions and for exploring the most common (and some not-so-common) probability distributions and their relationships to each other. The design philosophy focuses on developing intuition through exploration. It uses web technologies such as JavaScript and D3 graphics to implement several novel features, including: An intuitive interface for exploring the shapes of twenty-nine probability mass and density functions. Editing parameters using either text or sliders. Both automatic and manual control over axis scaling. Dynamic loading of examples illustrating the range of shapes distributions can take. Interactive exploration of the relationships between distributions through transformation of variables, summing variables, sampling, and limiting distributions. Interactive visualizations of the processes generating each distribution. Probability Playground also provides proofs for the mean and variance of each distribution and over 100 proofs for the relationships between distributions. I hope it's useful to you, and would welcome any comments, suggestions for improvement, or compliments!

Probability Playground is an interactive tool for exploring the most common (and some not-so-common) probability distributions and their relationships to each other. It uses web technologies such as JavaScript and D3 graphics to implement several novel features, including: An intuitive interface for exploring the shapes of twenty-nine probability mass and density functions. Editing parameters using either text or sliders. Both automatic and manual control over axis scaling. Dynamic loading of examples illustrating the range of shapes distributions can take. Interactive exploration of the relationships between distributions through transformation of variables, summing variables, sampling, and limiting distributions. Interactive visualizations of the processes generating each distribution.

Reference Material

This site would be useful for self-guided study/review and individual student practice, and also for professional interest in probability distribution.

This material can be used in variety of settings - in-class, homework, inidvidual explorations, lecture demonstrations of probability distributions. This material can also be used independently by students for building an intuitive understanding of the probability distributions

The application was created using JavaScript and D3 graphics technologies and needs a browser to render. The user would need to be connected to the internet to access the website.

The design philosophy focuses on developing intuition through exploration.

The major learning goals as enumerated by the creator on the "About" section as questions:

1. What kinds of shapes can the graphs of the distributions take, and how do these shapes depend on the parameters?

2. How do the distributions arise naturally?

3. If one distribution converges to another distribution, under what circumstances is it a good approximation?

4. If one distribution is a special case of another, how do the shapes of their probability mass or density functions compare?

5. If one distribution is a transformation of another, how does it change as the shape of the other distribution changes?

6. If one distribution is derived from a sample of another distribution, how does its shape change as the sample size increases?

High School, College General Ed, College Lower Division, College Upper Division, Graduate School, Students in an probability class. Faculty members and Professionals

Elementary probability.