Probability Theory

Overview

This course on Probability Theory aims to help learners understand the fundamental concepts and principles of probability. By the end of the course, students will be able to analyze and solve problems related to probability measures, discrete and continuous cases, binomial and hypergeometric distributions, conditional probability, Bayes's Theorem, random variables, and expectation. The course utilizes a structured approach with 15 parts covering various topics in probability theory. It is suitable for individuals interested in gaining a solid foundation in probability theory and its applications.

Syllabus

Probability Theory - Part 1 - Introduction.
Probability Theory - Part 2 - Probability Measures.
Probability Theory - Part 3 - Discrete vs. Continuous Case.
Probability Theory - Part 4 - Binomial Distribution.
Probability Theory - Part 5 - Product Probability Spaces.
Probability Theory - Part 6 - Hypergeometric Distribution.
Probability Theory - Part 7 - Conditional Probability.
Probability Theory - Part 8 - Bayes's Theorem and Total Probability.
Probability Theory - Part 9 - Independence for Events.
Probability Theory - Part 10 - Random Variables.
Probability Theory - Part 11 - Distribution of a Random Variable.
Probability Theory - Part 12 - Cumulative Distribution Function.
Probability Theory - Part 13 - Independence for Random Variables.
Probability Theory - Part 14 - Expectation and Change-of-Variables.
Probability Theory - Part 15 - Properties of the Expectation.