# A rigorous introduction to probability theory

These lectures by Michal Fabinger introduce basic concepts of probability theory in an intuitive yet rigorous way. This material should later help the participants understand scientific articles that use probability theory and statistics. Such knowledge is useful both for

machine-learning and data-science practitioners and for those on an

academic path (undergraduates, graduate students, postdocs, or faculty members). The content is similar to the corresponding course at the Acalonia school. All lectures are available on YouTube.

A rigorous introduction to probability theory – Lecture 1

Types of probability distributions and the need for a rigorous

mathematical framework. Probability spaces, sample spaces, event

spaces, and probability measures. Examples of probability spaces.

A rigorous introduction to probability theory 2:

Sigma-algebras for events. Borel sigma-algebras for events

corresponding to continuous sample spaces. Random variables. Examples of random variables.

A rigorous introduction to probability theory 3:

Distributions of random variables. Cumulative distribution functions,

probability mass functions, and probability density functions.

Examples of distributions.

A rigorous introduction to probability theory 4:

Transformations of random variables. Transformations of cumulative

distribution functions, probability mass functions, and probability

density functions. Examples of usage of transformed random variables.

Lectures by: Michal Fabinger

Twitter: https://twitter.com/fabinger

Bio: Michal is the founder of the Acalonia school (acalonia.com,

formerly tokyodatascience.com), which aims to build an education

system for a world where location does not matter. The school provides a straightforward way for talented people from developed and developing countries to improve their skills for their current jobs,

get new knowledge-demanding jobs, or get admitted to graduate schools. The Fair Play Tuition system (acalonia.com/fair-play) makes this possible even for those who currently lack finances. Michal's research is in physics and economics, with the corresponding PhD training completed at Stanford and Harvard. At the University of Tokyo and the Pennsylvania State University, Michal taught courses on Deep Learning, Data Science, Statistics, Asset Pricing, International Trade,

International Finance, and Development Economics.