In this video, we aim to construct random number generators of any probability distribution. We introduce the theory of random variables and transform of random variables in order to construct random number generators of any distribution.

In this video, the linear congruential generator is introduced.
https://en.wikipedia.org/wiki/Linear_...

However, the much more popular method used today is the Mersenne Twister, which is significantly harder to understand, and it is beyond the scope of this video.
https://en.wikipedia.org/wiki/Mersenn...

Two main techniques used in this video are the probability integral transform and the inverse transform sampling.
https://en.wikipedia.org/wiki/Probabi...
https://en.wikipedia.org/wiki/Inverse...

My other video on a more rigorous definition of random variables:
   • Mathematics of Maximizing Profit in G...  

Chapters:
00:00 Intro
02:38 Continuous Distributions
05:19 General Theory of Random Variables
07:47 Piecewise Linear Transformation of Random Variables
10:10 Nonlinear Transformation of Random Variables
13:06 Geometry of Transformation of Random Variables
16:24 Linear Congruential Generator
19:54 Probability Integral Transform and Inverse Transform Sampling
23:30 Generalized Inverse
25:06 Transform Between Any Two Distributions
26:13 Outro

Music:
Titanium Mittsies    • Mittsies  Titanium  
Pocket's Lookin' Light Gareth Coker · Riot Forge    • Pocket's Lookin' Light  
Runnin' From Lariette Gareth Coker · Riot Forge    • Runnin' From Lariette  
Machina del Diablo Stephen Rippy
Driftveil City Funk Cover Sean R. Hanson    • Pokemon BW  Driftveil City  Funk Cover  

Corrections:
19:45 Mersenne Twister is not the best RNG today
22:56 CDF not PDF