Probability Theory: Foundation for Data Science

Anne Dougherty

Offered By

Probability Theory: Foundation for Data Science

University of Colorado Boulder

About this Course

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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) degree offered on the Coursera platform. The MS-DS is an interdisciplinary degree that brings 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 MS-DS is 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.

Logo adapted from photo by Christopher Burns on Unsplash.

Flexible deadlines

Reset deadlines in accordance to your schedule.

Shareable Certificate

Earn a Certificate upon completion

100% online

Start instantly and learn at your own schedule.

Intermediate Level

Sequence in calculus up through Calculus II (preferably multivariate calculus) and some programming experience in R.

Approx. 48 hours to complete

English

Subtitles: English

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

Probabilitycentral limit theoremcontinuous random variablesBayes' Theoremdiscrete random variables

Flexible deadlines

Reset deadlines in accordance to your schedule.

Shareable Certificate

Earn a Certificate upon completion

100% online

Start instantly and learn at your own schedule.

Intermediate Level

Sequence in calculus up through Calculus II (preferably multivariate calculus) and some programming experience in R.

Approx. 48 hours to complete

English

Subtitles: English

Instructor

Anne Dougherty

Senior Instructor and Teaching Professor

Applied Mathematics

1,079 Learners

1 Course

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.

Syllabus - What you will learn from this course

Week

Week 1

9 hours to complete

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.

9 hours to complete

3 videos (Total 51 min), 3 readings, 3 quizzes

Week

Week 2

7 hours to complete

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.

7 hours to complete

2 videos (Total 52 min), 1 reading, 3 quizzes

Week

Week 3

8 hours to complete

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.

8 hours to complete

4 videos (Total 78 min), 1 reading, 3 quizzes

Week

Week 4

9 hours to complete

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.

9 hours to complete

4 videos (Total 97 min), 2 readings, 3 quizzes

Frequently Asked Questions

When will I have access to the lectures and assignments?
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The course may offer 'Full Course, No Certificate' instead. This option lets you see all course materials, submit required assessments, and get a final grade. This also means that you will not be able to purchase a Certificate experience.
What will I get if I purchase the Certificate?
When you purchase a Certificate you get access to all course materials, including graded assignments. Upon completing the course, your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.
Is financial aid available?
Yes, Coursera provides financial aid to learners who cannot afford the fee. Apply for it by clicking on the Financial Aid link beneath the "Enroll" button on the left. You’ll be prompted to complete an application and will be notified if you are approved. Learn more.
Will I earn university credit for completing the Course?
This Course doesn't carry university credit, but some universities may choose to accept Course Certificates for credit. Check with your institution to learn more. Online Degrees and Mastertrack™ Certificates on Coursera provide the opportunity to earn university credit.

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Probability Theory: Foundation for Data Science

Probability Theory: Foundation for Data Science