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