Probability Foundations for Data Science and AI
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Probability Foundations for Data Science and AI
This course is part of multiple programs.
Instructors: Anne Dougherty
40,334 already enrolled
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290 reviews
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290 reviews
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What you'll 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.
Details to know
7 assignments
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There are 6 modules in this course
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 can be taken for academic credit as part of CU Boulder’s Master of Science in Data Science (MS-DS) and the Master of Science in Artificial Intelligence (MS-AI) degrees offered on the Coursera platform. These interdisciplinary degrees bring together faculty from CU Boulder’s departments of Applied Mathematics, Computer Science, Information Science, and others. With performance-based admissions and no application process, the CU degrees on Coursera are ideal for individuals with a broad range of undergraduate education and/or professional experience in computer science, information science, mathematics, and statistics. Learn more about the MS-DS program at https://www.coursera.org/degrees/master-of-science-data-science-boulder. Learn more about the MS-AI program at https://www.coursera.org/degrees/ms-artificial-intelligence-boulder Logo adapted from photo by Christopher Burns on Unsplash.
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.
What's included
6 videos6 readings2 assignments1 programming assignment2 ungraded labs
6 videos•Total 78 minutes
- Intro to Probability•14 minutes
- Axioms of Probability•20 minutes
- Counting: Permutations and Combinations•18 minutes
- License Plate Counting Problem•7 minutes
- Estimating Probability•10 minutes
- Probability of Answering a Question Correctly•10 minutes
6 readings•Total 141 minutes
- Course Updates and Accessibility Support•1 minute
- Earn Academic Credit for your Work!•10 minutes
- Course Support•10 minutes
- Course Resources and Reading•10 minutes
- Intro to Probability•100 minutes
- Introducing the formula sheet for this course•10 minutes
2 assignments•Total 50 minutes
- AI Policy Quiz•5 minutes
- Homework: Descriptive Statistics and the Axioms of Probability•45 minutes
1 programming assignment•Total 180 minutes
- Homework: Axioms of Probability•180 minutes
2 ungraded labs•Total 120 minutes
- Introduction to Jupyter Notebooks and R•60 minutes
- Guided Exploratory Ungraded Lab•60 minutes
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.
What's included
2 videos1 reading1 assignment1 programming assignment1 ungraded lab
2 videos•Total 52 minutes
- Conditional Probability and Bayes Theorem•25 minutes
- Independent Events•28 minutes
1 reading•Total 60 minutes
- Conditional Probability and Bayes Theorem•60 minutes
1 assignment•Total 30 minutes
- Homework: Conditional Probability•30 minutes
1 programming assignment•Total 180 minutes
- Homework: Bayes Theorem •180 minutes
1 ungraded lab•Total 60 minutes
- Guided Exploratory Ungraded Lab•60 minutes
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.
What's included
4 videos1 reading1 assignment1 programming assignment1 ungraded lab
4 videos•Total 78 minutes
- Discrete Random Variables•20 minutes
- Bernoulli and Geometric Random Variables•11 minutes
- Expectation and Variance•21 minutes
- Binomial and Negative Binomial Random Variables•25 minutes
1 reading•Total 60 minutes
- Discrete Random Variables•60 minutes
1 assignment•Total 45 minutes
- Homework: Discrete Random Variables•45 minutes
1 programming assignment•Total 180 minutes
- Homework: Calculations with Discrete Random Variables•180 minutes
1 ungraded lab•Total 60 minutes
- Guided Exploratory Ungraded Lab•60 minutes
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.
What's included
4 videos2 readings1 assignment1 programming assignment1 ungraded lab
4 videos•Total 97 minutes
- Continuous Random Variables•22 minutes
- The Gaussian (normal) Random Variable Part 1•19 minutes
- The Normal Random Variable Part 2•27 minutes
- The Poisson and Exponential Random Variables•29 minutes
2 readings•Total 120 minutes
- Continuous random variables•60 minutes
- Normal Random Variable•60 minutes
1 assignment•Total 30 minutes
- Homework: Continuous Random Variables•30 minutes
1 programming assignment•Total 180 minutes
- Homework: Continuous Random Variables and Normal Random Variables•180 minutes
1 ungraded lab•Total 60 minutes
- Guided Exploratory Ungraded Lab•60 minutes
The power of statistics lies in being able to study the outcomes and effects of multiple random variables (i.e. sometimes referred to as “data”). Thus, in this module, we’ll learn about the concept of “joint distribution” which allows us to generalize probability theory to the multivariate case.
What's included
3 videos1 reading1 assignment1 programming assignment
3 videos•Total 66 minutes
- Covariance and Correlation•35 minutes
- More on Expectation and Variance•16 minutes
- Jointly Distributed Random Variables•16 minutes
1 reading•Total 60 minutes
- Covariance and Correlation•60 minutes
1 assignment•Total 30 minutes
- Homework: Joint Distributions and Covariance•30 minutes
1 programming assignment•Total 180 minutes
- Homework: Calculations of Covariance and Correlation in Various Examples•180 minutes
The Central Limit Theorem (CLT) is a crucial result used in the analysis of data. In this module, we’ll introduce the CLT and it’s applications such as characterizing the distribution of the mean of a large data set. This will set the stage for the next course.
What's included
2 videos1 reading1 assignment1 programming assignment1 ungraded lab
2 videos•Total 40 minutes
- Introduction to the Central Limit Theorem•20 minutes
- Central Limit Theorem Examples•20 minutes
1 reading•Total 60 minutes
- Central Limit Theorem•60 minutes
1 assignment•Total 30 minutes
- Homework: Central Limit Theorem•30 minutes
1 programming assignment•Total 180 minutes
- Homework: Working with Normal Random Variables and the CLT•180 minutes
1 ungraded lab•Total 60 minutes
- Guided Exploratory Ungraded Lab•60 minutes
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This course is part of the following degree program(s) offered by University of Colorado Boulder. If you are admitted and enroll, your completed coursework may count toward your degree learning and your progress can transfer with you.¹
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Reviewed on Jun 2, 2024
Thank you to everyone who put a lot of effort into making this course; it is really helpful.
Reviewed on May 4, 2025
I would suggest to provide coding videos or solution for such coding problems so that we can easily understand and solve the questions
Reviewed on Mar 4, 2023
This course taught me the basics of probability, R programming, and Latex. I am deeply grateful to Prof. Anne Dougherty, UC Boulder, and Coursera for this tough but wonderful experience.
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