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3blue1brown
3blue1brown
@3blue1brown·8.4M subscribers·238 videos

A pretty reason why Gaussian + Gaussian = Gaussian

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July 11, 2023

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Chapters

Segments

youtu.be/zeJD6dqJ5loyoutu.be/cy8r7WSuT1Iyoutu.be/IaSGqQa5O-M

YouTube Description

as posted by the channel

A visual trick to compute the sum of two normally distributed variables.

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Help fund future projects

Special thanks to these supporters

For the technically curious who want to go deeper, here's a proof of the central limit theorem using Moment generating functions:

And here's a nice discussion of methods using entropy:

Relevant previous videos

Central limit theorem

Why π is there, and the Herschel-Maxwell derivation

Convolutions and adding random variables

Time stamps

Thanks to these viewers for their contributions to translations

German: lprecord, qoheniac

Spanish: Pablo Asenjo Navas-Parejo

Vietnamese: Duy Tran

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These animations are largely made using a custom Python library, manim. See the FAQ comments here:

You can find code for specific videos and projects here:

Music by Vincent Rubinetti.

Download the music on Bandcamp:

Stream the music on Spotify:

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3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe

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Guests & Subjects Covered

Central Limit TheoremVincent Rubinetti DownloadBandcamp Stream

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