Probability

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INTRODUCTION

I wrote about Claude Shannon who used Markov chains in information theory. See http://www.kinberg.net/wordpress/stellan/equations/#informationtheory

INDEX

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Conditional probability

Where event probability depends on other events. So the events are dependent.

https://www.mathsisfun.com/data/probability-events-conditional.html

Can be illustrated with a Bayesian network like this:

Another good course is this:

Origins of Markov chains is explained by Khan Academy

Everything in the world is governed by precise ratios and a constant law of change.

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Shannon information theory

See http://www.kinberg.net/wordpress/stellan/equations/#informationtheory

 

I dont know why Edward Witten choose to start with a short introduction to Communication theory (the Shannon theory) at “Theoretical Physics 2018: From Qubits to Spacetime”

I presume it is important to know about this, to understand the theory of Quantum mechanics and aspects of General Relativity as he says to continue with at the conference.
I decided to take a look at C.E. Shannons book from 1948 ” A mathematical theory of Communication

Shannon was an American mathematician, electrical engineer, and cryptographer known as “the father of information theory“. He wrote also “Theoretical Genetics.”[12]

A mathematical theory of Communication – Shannon theory
 
Khan Academy has a great introduction to Shannons theory in this video: (in youtube settings choose your subtitle language).
the video with English text is here.
 
 
C.E. Shannons book from 1948 ” A mathematical theory of Communication“. The instructor in this Khan video says among others:
“Claude Elwood Shannon developed theory about cryptography. Then Claude Shannon demonstrated how to generate “English looking” text using  Markov chains.
Bernouilli. Weak law of large number says: As the number of trials increases, the expected ratio value will converge on the actual underlying ratio. He refined the idea of expectation. If observations of all the events will be continued for the entire infinity it will be noticed that “Everything in the world is governed by precise ratios and a constant law of change.”
The binomial distribution appears to be an ideal form as it kept appearing everywhere anytime  you looked at a the variation of a large number of random trials. It seems the average fate of these events are somehow predetermined, known today as  “The central limit theorem”
Most of things in the physical world are clearly dependent on prior  outcomes. We talk about dependent events or dependent variables.
Markov prooved that independent and dependent events can converge on predictable distributions.
One of the most famous application of Markov chains was published by Claude Shannon.”

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conclusion

 


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 Proba

A agnostic pluralist seeker

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