L01.1 - Overview of Probability Models and Axioms
Video: https://youtu.be/1uW3qMFA9Ho?si=lsQUp-E_ByLeDGLy
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Table of Contents:
A) What is a Probabilistic Model?
A probabilistic model is a quantitative description of a situation, a phenomenon, or an experiment whose outcome is uncertain.
A.1) How to build a Probabilistic Model?
Putting together such a model involves two key steps:
1st step - Sample Space:
We need to describe the possible outcomes of the experiment.
This is done by specifying a so-called "Sample Space".
2nd step - Probability Law:
We need to specify a "probability law", which assigns probabilities to outcomes (or to collections of outcomes).
The Probability Law tells us, for example, whether one outcome is much more likely
than some other outcome.
B) The Axioms of Probability Theory
"Probabilities" have to satisfy certain basic properties in order to be meaningful.
These are the axioms of probability theory,
For example, from axiom 1, we can see that probabilities cannot be negative.
Interestingly, there will be very few axioms, but they are very powerful and we will see that they have lots of consequences.
We will see that axioms imply many other properties that were not part of the axioms.
C) Discrete and Continuous Random Variables
We will then go through a couple of very simple examples involving models with either discrete or continuous outcomes.
You will see many times that discrete models are conceptually much easier.
Continous models involve some more sophisticated concepts.
D) The Big Picture
And finally, we will talk a little bit about the big picture, about the role of probability theory, and its relation with the real world.
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Z) 🗃️ Glossary
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