A pretty reason why Gaussian + Gaussian = Gaussian

From the creator

A visual trick to compute the sum of two normally distributed variables. 3b1b mailing list: https://3blue1brown.substack.com/ Help fund future projects: https://www.patreon.com/3blue1brown Special thanks to these supporters: https://www.3blue1brown.com/lessons/gaussian-convolution#thanks For the technically curious who want to go deeper, here's a proof of the central limit theorem using Moment generating functions: https://www.cs.toronto.edu/~yuvalf/CLT.pdf And here's a nice discussion of methods using entropy: https://mathoverflow.net/questions/182752/central-limit-theorem-via-maximal-entropy Relevant previous videos Central limit theorem https://youtu.be/zeJD6dqJ5lo Why π is there, and the Herschel-Maxwell derivation https://youtu.be/cy8r7WSuT1I Convolutions and adding random variables https://youtu.be/IaSGqQa5O-M Time stamps 0:00 - Recap on where we are 2:10 - What direct calculation would look like 3:38 - The visual trick 8:27 - How this fits into the Central Limit Theorem 12:30 - Mailing list Thanks to these viewers for their contributions to translations German: lprecord, qoheniac Spanish: Pablo Asenjo Navas-Parejo Vietnamese: Duy Tran ------------------ These animations are largely made using a custom Python library, manim. See the FAQ comments here: https://www.3blue1brown.com/faq#manim https://github.com/3b1b/manim https://github.com/ManimCommunity/manim/ You can find code for specific videos and projects here: https://github.com/3b1b/videos/ Music by Vi

Published 2023-07-11 · Watch on YouTube ↗
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