Understand the foundations of probability and its relationship to statistics and data science. We’ll learn what it means to calculate a probability, independent and dependent outcomes, and conditional events. We’ll study discrete and continuous random variables and see how this fits with data collection. We’ll end the course with Gaussian (normal) random variables and the Central Limit Theorem and understand its fundamental importance for all of statistics and data science.
This course is part of the Data Science Foundations: Statistical Inference Specialization
Offered By
About this Course
Sequence in calculus up through Calculus II (preferably multivariate calculus) and some programming experience in R.
What you will learn
Explain why probability is important to statistics and data science.
See the relationship between conditional and independent events in a statistical experiment.
Calculate the expectation and variance of several random variables and develop some intuition.
Skills you will gain
- Probability
- central limit theorem
- continuous random variables
- Bayes' Theorem
- discrete random variables
Sequence in calculus up through Calculus II (preferably multivariate calculus) and some programming experience in R.
Offered by

University of Colorado Boulder
CU-Boulder is a dynamic community of scholars and learners on one of the most spectacular college campuses in the country. As one of 34 U.S. public institutions in the prestigious Association of American Universities (AAU), we have a proud tradition of academic excellence, with five Nobel laureates and more than 50 members of prestigious academic academies.
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Syllabus - What you will learn from this course
Descriptive Statistics and the Axioms of Probability
Understand the foundation of probability and its relationship to statistics and data science. We’ll learn what it means to calculate a probability, independent and dependent outcomes, and conditional events. We’ll study discrete and continuous random variables and see how this fits with data collection. We’ll end the course with Gaussian (normal) random variables and the Central Limit Theorem and understand it’s fundamental importance for all of statistics and data science.
Conditional Probability
The notion of “conditional probability” is a very useful concept from Probability Theory and in this module we introduce the idea of “conditioning” and Bayes’ Formula. The fundamental concept of “independent event” then naturally arises from the notion of conditioning. Conditional and independent events are fundamental concepts in understanding statistical results.
Discrete Random Variables
The concept of a “random variable” (r.v.) is fundamental and often used in statistics. In this module we’ll study various named discrete random variables. We’ll learn some of their properties and why they are important. We’ll also calculate the expectation and variance for these random variables.
Continuous Random Variables
In this module, we’ll extend our definition of random variables to include continuous random variables. The concepts in this unit are crucial since a substantial portion of statistics deals with the analysis of continuous random variables. We’ll begin with uniform and exponential random variables and then study Gaussian, or normal, random variables.
Reviews
- 5 stars66.17%
- 4 stars17.64%
- 3 stars2.94%
- 2 stars2.94%
- 1 star10.29%
TOP REVIEWS FROM PROBABILITY THEORY: FOUNDATION FOR DATA SCIENCE
Need to brush up integral calculus for thios course. Something I haven't looked at for 40 years.
The instructor is very good, more examples need to be added, there are mistakes in the evaluation
This is a great course on probability. Although I felt like it was too easy and should include more PDFs (such as Beta and Gamma) and random variable transformations.
About the Data Science Foundations: Statistical Inference Specialization
This program is designed to provide the learner with a solid foundation in probability theory to prepare for the broader study of statistics. It will also introduce the learner to the fundamentals of statistics and statistical theory and will equip the learner with the skills required to perform fundamental statistical analysis of a data set in the R programming language.

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