University of Colorado Boulder
Probability Theory: Foundation for Data Science
University of Colorado Boulder

Probability Theory: Foundation for Data Science

Anne Dougherty
Jem Corcoran

Instructors: Anne Dougherty

23,891 already enrolled

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Course

Gain insight into a topic and learn the fundamentals

4.5

(160 reviews)

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90%

Intermediate level

Recommended experience

42 hours (approximately)
Flexible schedule
Learn at your own pace
Progress towards a degree

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

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Assessments

6 quizzes

Taught in English

Course

Gain insight into a topic and learn the fundamentals

4.5

(160 reviews)

|

90%

Intermediate level

Recommended experience

42 hours (approximately)
Flexible schedule
Learn at your own pace
Progress towards a degree

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This course is part of the Data Science Foundations: Statistical Inference Specialization
When you enroll in this course, you'll also be enrolled in this Specialization.
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There are 7 modules in this course

Welcome to the course! This module contains logistical information to get you started!

What's included

6 readings1 app item1 discussion prompt1 ungraded lab

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

3 videos3 readings1 quiz1 programming assignment1 ungraded lab

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 videos2 readings1 quiz1 programming assignment1 ungraded lab

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 videos2 readings1 quiz1 programming assignment1 ungraded lab

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 videos3 readings1 quiz1 programming assignment1 ungraded lab

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 videos2 readings1 quiz1 programming assignment

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 videos3 readings1 quiz1 programming assignment1 ungraded lab

Instructors

Instructor ratings
4.8 (58 ratings)
Anne Dougherty
University of Colorado Boulder
2 Courses24,075 learners
Jem Corcoran
University of Colorado Boulder
6 Courses27,017 learners

Offered by

Recommended if you're interested in Probability and Statistics

Get a head start on your degree

This course is part of the following degree programs offered by University of Colorado Boulder. If you are admitted and enroll, your coursework can count toward your degree learning and your progress can transfer with you.

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4.5

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JB
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Reviewed on Dec 9, 2022

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Reviewed on Jun 2, 2024

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