Probability Theory: Foundation for Data Science from Coursera

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

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What's inside

Syllabus

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

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.

Joint Distributions and Covariance

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.

The Central Limit Theorem

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.

Good to know

Know what's good

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, and possible dealbreakers

Teaches probability, which is a foundational concept for data science and statistics

Develops mathematical foundations that support the study of statistics and data science

Provides a gentle introduction to a complex field through approachable activities and lessons

Examines discrete and continuous random variables, which are crucial concepts for data analysis

Explores the Central Limit Theorem, which is a fundamental result used in data analysis and modeling

Reviews summary

Comprehensive probability foundations

learners say this course provides a strong foundational learning experience in probability. Engaging assignments, including quizzes, programming, and peer-rated projects, reinforce the well-presented lectures and readings. Students appreciate the clear explanations and examples, but some note the difficulty of the exams and the lack of feedback on auto-graded homework.

Provides a good introduction to R programming.

"This course taught me the basics of probability, R programming, and Latex."

"Good combination between theory and practice."

Offers a logical arrangement of detailed, practical lectures, readings, and homework that build off each other.

"The material was well thought/planned out such that the readings, lectures, and homeworks built off each other in a constructive manner, which reinforced the material."

"This is very good and well prepared course."

"If we can have a section to bring R programming and the Math together that would be even better."

Features helpful quizzes, interesting projects, and challenging programming assignments.

"Excellent Review of probability. Interesting quizzes and projects."

"I really appreciate the number and depth of the exercises for each module."

"This course taught me the basics of probability, R programming, and Latex."

Exams can be difficult.

"Rounding could be the reason for homework mistakes"

"Need to brush up integral calculus for thios course. Something I haven't looked at for 40 years."

The provided textbook is not well-received by some.

"I really did not like the textbook that was provided."

"It is supposed to be different from a traditional text book, in a way that makes it easier to understand, I guess. But honestly I thought it had the opposite effect."

"I ended up searching for other online sources for better explanations of what was going on."

Homework is auto-graded without providing specific feedback on incorrect answers.

"The only downside is the auto-grading of the homework doesn't tell you which question you got wrong, so that can be frustrating."

"All you get is the number of cells that didn't pass; when you reload the assignment, there is no indication of what was wrong."

"The grader gives zero feedback regarding what was incorrect, not to mention why or what the correct answer is."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Probability Theory: Foundation for Data Science with these activities:

Review probability theory

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Brings existing probability theory knowledge up to date and will help reinforce concepts.

View Introduction to Probability Models on Amazon

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Review the axioms of probability
Solve practice problems on probability
Summarize key concepts in probability theory

Solve practice problems on probability distributions

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Helps reinforce understanding of probability distributions by providing targeted practice on a variety of problem types.

Browse courses on Probability Distributions

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Identify the type of probability distribution
Calculate probabilities using the probability mass function or probability density function
Solve word problems involving probability distributions

Create a data analysis project on real-world data

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Provides a practical application of probability and statistics concepts to real-world data.

Browse courses on Data Analysis

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Identify a real-world dataset
Clean and prepare the data
Apply probability and statistics techniques to analyze the data
Create visualizations to present the results
Write a report summarizing the findings

Five other activities

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Show all eight activities

Write a blog post on a probability or statistics topic

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Requires students to synthesize their understanding of probability and statistics concepts and communicate them to others.

Browse courses on Probability

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Choose a probability or statistics topic
Research the topic
Write a blog post explaining the topic in a clear and concise way
Proofread and edit the blog post
Publish the blog post

Follow tutorials on Bayesian statistics

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Provides a deeper dive into Bayesian statistics, a powerful technique used in probability and data analysis.

Browse courses on Bayesian Statistics

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Find tutorials on Bayesian statistics
Follow the tutorials
Implement Bayesian statistical methods in practice

Attend a workshop on data visualization

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Provides hands-on experience and exposure to best practices in data visualization, a key skill for data analysis.

Browse courses on Data Visualization

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Find a workshop on data visualization
Attend the workshop

Volunteer with a data science or statistics organization

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Offers practical experience in applying probability and statistics concepts in a real-world setting.

Browse courses on Data Science

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Find a data science or statistics organization to volunteer with
Apply to volunteer
Participate in volunteer activities

Participate in a data science or statistics competition

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Provides a challenging and motivating way to apply probability and statistics skills in a competitive setting.

Browse courses on Data Science

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Find a data science or statistics competition
Register for the competition
Prepare for the competition
Participate in the competition

Career center

Learners who complete Probability Theory: Foundation for Data Science will develop knowledge and skills that may be useful to these careers:

Statistician

The Probability Theory: Foundation for Data Science course alligns well with the field of Statistics. It covers the mathematical and statistical principles of probability and their applications in data analysis and modeling, providing a strong foundation for aspiring Statisticians.

See salaries and explore the career path for Statistician

Actuary

An understanding of probability is essential for Actuaries. The Probability Theory: Foundation for Data Science course covers the concepts and techniques involved in calculating probabilities, which is fundamental to actuarial work in assessing risks and making financial projections.

See salaries and explore the career path for Actuary

Data Scientist

A Probability Theory: Foundation for Data Science course can prove useful to those aspiring to be Data Scientists. It covers the basics of probability and its relevance in data science. This course can be particularly helpful in making sense of data and drawing meaningful conclusions from it. Additionally, it provides a solid foundation for more advanced topics such as machine learning and artificial intelligence.

See salaries and explore the career path for Data Scientist

Statistical Analyst

As the title suggests, Probability Theory: Foundation for Data Science can be a valuable asset for aspiring Statistical Analysts. It delves into the fundamentals of probability and its applications in data analysis, which provides a good grounding for the analysis and interpretation of data.

See salaries and explore the career path for Statistical Analyst

Applied Statistician

Probability Theory: Foundation for Data Science is highly relevant to Applied Statisticians. It covers the concepts and techniques of probability and their applications in real-world data analysis and modeling. This course can provide Applied Statisticians with a strong foundation for their work.

See salaries and explore the career path for Applied Statistician

Machine Learning Engineer

A Probability Theory: Foundation for Data Science course can be a valuable asset for Machine Learning Engineers. It covers the mathematical foundations of probability and statistics, which are essential for understanding and developing machine learning algorithms.

See salaries and explore the career path for Machine Learning Engineer

Risk Analyst

The Probability Theory: Foundation for Data Science course aligns well with the field of Risk Analysis. It covers the principles of probability and its use in assessing and managing risks. This course can provide aspiring Risk Analysts with a strong theoretical foundation for their work.

See salaries and explore the career path for Risk Analyst

Data Analyst

The Probability Theory: Foundation for Data Science course offers a solid foundation for aspiring Data Analysts. It covers the principles of probability and its use in data analysis and interpretation, which are essential skills for Data Analysts in extracting insights from data.

See salaries and explore the career path for Data Analyst

Quantitative Analyst

A Probability Theory: Foundation for Data Science course is highly relevant to those aspiring to be Quantitative Analysts. It covers the mathematical and statistical concepts used in financial modeling and risk assessment, which are essential skills for Quantitative Analysts.

See salaries and explore the career path for Quantitative Analyst

Data Engineer

Probability Theory: Foundation for Data Science offers relevant knowledge for Data Engineers. It provides a comprehensive overview of probability and its applications in data analysis and management, which are essential skills for Data Engineers in designing and implementing data pipelines.

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Operations Research Analyst

For those interested in becoming Operations Research Analysts, a Probability Theory: Foundation for Data Science course can be beneficial. It provides a solid understanding of probability and its applications in modeling and optimizing systems, which is crucial for Operations Research Analysts in analyzing and improving complex processes.

See salaries and explore the career path for Operations Research Analyst

Business Analyst

Business Analysts often rely on data to make informed decisions. Having a strong foundation in probability can enable them to better understand and analyze data. The Probability Theory: Foundation for Data Science course can provide that foundation, equipping Business Analysts with the skills to extract meaningful insights from data.

See salaries and explore the career path for Business Analyst

Software Engineer

For Software Engineers pursuing roles in data-intensive fields, Probability Theory: Foundation for Data Science can be helpful. It provides a solid understanding of probability and its applications in data analysis and modeling, which can be beneficial in designing and developing software solutions for data-driven applications.

See salaries and explore the career path for Software Engineer

Financial Analyst

Probability Theory: Foundation for Data Science can be a helpful resource for aspiring Financial Analysts. It covers the principles of probability and its use in financial modeling and analysis, which can provide a strong foundation for understanding financial markets and making investment decisions.

See salaries and explore the career path for Financial Analyst

Economist

Economists often use probability and statistics to analyze economic data and make predictions. The Probability Theory: Foundation for Data Science course can provide a strong foundation in probability and its applications in economics, which can be beneficial for aspiring Economists.

See salaries and explore the career path for Economist