Probability Theory & Statistics Fundamentals

Probability Theory & Statistics Fundamentals free download

University level course in probability theory and statistics appropriate for students and social scientists

What are the chances of your decision being right—or disastrously wrong? Probability and statistics provide the mathematical lens to make sense of an unpredictable world. In this course, you’ll discover how randomness, risk, and patterns of data are not just chaos, but deeply structured phenomena you can model, analyze, and predict.

Whether you're preparing for advanced econometrics, diving into data science, or simply want to sharpen your analytical thinking, this course, with 64 lectures and over 60 downloadable PDF resources accompanying the lectures walks you step-by-step from probability theory fundamentals to real-world statistical inference. With a rigorous yet accessible approach, you’ll gain the tools to confidently interpret uncertainty and make smarter decisions.

Ready to decode randomness and take control of data? Let’s get started.

What You’ll Learn:

Probability – Building the Foundation

We begin with the essential building blocks: experiments, outcomes, and events. From there, we rigorously define probability and conditional probability, giving you the tools to model uncertainty mathematically. The chapter concludes with a discussion on independent events — a concept central to understanding real-world randomness.

Random Variables – The Heart of Probability Theory

Random variables are the bridge between probability theory and measurable outcomes. We’ll explore what random variables are, how to work with their distribution functions, and why the standard normal distribution is the most studied of them all.

Moments – Understanding Behavior Through Functions

Moments provide critical insights into the behavior of random variables. This chapter introduces you to calculating moments, transformations of variables via functions (e.g., Y = g(X)), and the prominent family of normal random variables.

Multiple Random Variables – Beyond the Single Dimension

Dive into the rich world of working with multiple random variables. You'll learn how to define them on the same probability space, analyze their joint and conditional distributions, and calculate joint and conditional moments. We also cover key concepts such as covariance and the powerful law of iterated expectations.

Random Vectors – Compact Representations for Complex Systems

Extend your understanding to random vectors — multi-dimensional representations of random variables. This chapter introduces matrix notation to elegantly represent and manipulate functions of multiple variables, paving the way for more advanced applications in linear models and multivariate analysis.

Statistics – From Theory to Inference

We wrap up the course with a transition from pure probability to statistical inference. Learn how to draw conclusions about populations from samples using rigorous statistical methods. Key probability distributions and their relevance in statistical modeling are explored to equip you with a robust understanding of inference.

Why Take This Course?

University-Level Rigor: A structured and comprehensive introduction to probability and statistics

Application-Oriented: Designed for real-world applications in economics and social sciences

Mathematically Sound Yet Accessible: Balances theoretical depth with clear explanations

Step-by-Step Guidance: Progressively builds your knowledge with practical examples

Essential Foundation for Advanced Studies: Prepares you for more advanced courses in econometrics, data analysis, and research

Enroll Now and Master Probability & Statistics!

This course will equip you with the essential mathematical tools needed for data-driven decision-making in economics, business, and social sciences. Join today and take the first step toward mastering probability and statistics!

The lectures are provided by renowned econometrics lecturer, Peter Jochumzen from Lund University.