How to Construct Every Randomness | Transform of Random Variables, Random Number Generators скачать в хорошем качестве

How to Construct Every Randomness | Transform of Random Variables, Random Number Generators

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 Gambli...   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