Скачать или смотреть A pretty reason why Gaussian + Gaussian = Gaussian

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

And here's a nice discussion of methods using entropy:
https://mathoverflow.net/questions/18...

Relevant previous videos

Central limit theorem
   • But what is the Central Limit Theorem?  

Why π is there, and the Herschel-Maxwell derivation
   • Why π is in the normal distribution (beyon...  

Convolutions and adding random variables
   • Convolutions | Why X+Y in probability is a...  

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

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https://github.com/3b1b/manim
https://github.com/ManimCommunity/manim/

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Music by Vincent Rubinetti.
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