Full handwritten lecture notes can be downloaded from here:
https://drive.google.com/file/d/1iwPvb6sgVHbVEuVQEfEkpqHRPS4fTBXq/view?usp=sharing
Lecture 1
Introduction
Some examples of stochastic processes 5:55
Formal Definition of a Stochastic Process 23:34
Definition of a Probability Space 26:00
Definition of Sigma-Algebra (or Sigma-Field) 37:29
Definition of a Probability Measure 43:22
Introduction to Uncountable Probability Spaces: The Banach-Tarski Paradoxon 49:15
Definition of Borel-Sigma Field and Lebesgue Measure on Euclidean Space 53:14
Uniform Distribution on a bounded set in Euclidean Space, Example: Uniform Sampling from the unit cube. 1:00:53
Further Examples of countably or uncountable infinite probability spaces: Normal and Poisson distribution 1:03:23
A probability measure on the set of infinite sequences 1:13:46
Definition of Random Variables 1:21:44
Law of a Random Variable 1:25:42 and Examples