https://github.com/laszlokorte/random-variable

An interactive example of a function applied to a random variable showing the resulting distribution.
https://github.com/laszlokorte/random-variable

random-variables statistics

Last synced: 11 months ago
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An interactive example of a function applied to a random variable showing the resulting distribution.

• Host: GitHub
• URL: https://github.com/laszlokorte/random-variable
• Owner: laszlokorte
• Created: 2022-01-17T17:38:24.000Z (over 4 years ago)
• Default Branch: main
• Last Pushed: 2022-04-03T14:00:10.000Z (about 4 years ago)
• Last Synced: 2025-05-15T08:11:48.236Z (about 1 year ago)
• Topics: random-variables, statistics
• Language: Svelte
• Homepage: https://tools.laszlokorte.de
• Size: 54.7 KB
• Stars: 0
• Watchers: 2
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

          
![Screenshot of the app](preview.png)

[Live Demo](https://static.laszlokorte.de/random-variable/) | [Short demo video](https://www.youtube.com/watch?v=UGjjtJiGywk)

# Function applied to random variables

Applying a function to a random variable affects the resulting distribution. The colored rectangles represent the density of the random variable along the X axis. You can see how squaring the variable shifts all rectangles into the positive range. Each colored rectangles keeps its area but is stretched along the X axis by 2*x (the derivative of x2). Accordingly the height of each rectangle is compressed by 2*x to keep the area constant.

As x^2 is not injective multiple rectangles end up at the same target along the x axis. They simply stack on top of each other to represent the resulting probability density at each location.

Clicking on a single rectangle highlights its corresponding partner rectangle in the other distribution.

Lowering the number of bins makes the individual rectangles more recognizable but reduces the precision of the probability density.