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Introduction to Probability

5.0 Filled star Filled star Filled star Filled star Filled star
Based on 1 rating
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Joseph Blitzstein

Probability and statistics help to bring logic to a world replete with randomness and uncertainty. This course will give you tools needed to understand data, science, philosophy, engineering, economics, and finance. You will learn not only how to solve challenging technical problems, but also how you can apply those solutions in everyday life.

With examples ranging from medical testing to sports prediction, you will gain a strong foundation for the study of statistical inference, stochastic processes, randomized algorithms, and other subjects where probability is needed.

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What's inside

Learning objectives

  • How to think about uncertainty and randomness
  • How to make good predictions
  • The story approach to understanding random variables
  • Common probability distributions used in statistics and data science
  • Methods for finding the expected value of a random quantity
  • How to use conditional probability to approach complicated problems

Syllabus

Unit 0: Introduction, Course Orientation, and FAQ
Unit 1: Probability, Counting, and Story Proofs
Unit 2: Conditional Probability and Bayes' Rule
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Traffic lights

Read about what's good
what should give you pause
and possible dealbreakers
Explores probability and statistics in a practical way, providing real-world examples from fields like medicine and sports
Taught by Joseph Blitzstein, a recognized expert in probability and data science
Develops a strong foundation in probability for further study in statistical inference and other related fields
Suitable for beginners who want to build a solid foundation in probability and statistics
May require additional knowledge in mathematics, particularly calculus, for some sections
The course does not cover advanced topics in probability and statistics

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Reviews summary

Strong introduction to probability

According to learners, this course provides a solid foundation in probability theory, suitable for those entering quantitative fields. Many find the lectures to be exceptionally clear and well-structured, making complex topics accessible. However, students frequently note that the homework assignments can be quite challenging and that a prior background in calculus is very helpful, if not necessary, despite it being an introductory course. Overall, the sentiment is largely positive, with reviewers appreciating the depth and clarity, positioning it as an excellent starting point for further study.
Emphasis is on theoretical understanding.
"The course is quite theoretical, which is great for understanding the 'why'."
"Don't expect a lot of coding or practical applications; it's theory-heavy."
"I appreciate the deep dive into theoretical concepts rather than just formulas."
"Focuses strongly on mathematical proofs and concepts..."
Prior calculus knowledge is highly recommended.
"While listed as introductory, having some calculus background is very beneficial for me."
"You should be comfortable with basic calculus before starting this course; it helps a lot."
"I struggled a bit because my math skills weren't as strong as needed."
"Knowing calculus makes understanding the material much easier..."
Provides an excellent base for future studies.
"This course gave me a really solid foundation in probability theory."
"I feel much better prepared for advanced statistics courses now."
"It lays the groundwork excellently for data science and other quantitative areas, in my opinion."
"An essential course if you plan to study statistics or data science further."
Lectures are praised for clarity and structure.
"The instructor's explanations were incredibly clear, making complex topics easy to grasp."
"I found the lectures to be very well-structured and easy to follow."
"Everything is explained really well, building up step by step..."
"Complex concepts are broken down into understandable parts..."
Homework problems require significant effort.
"I found the homework problems very challenging, requiring significant effort."
"Some assignments took me a long time to solve; they were quite tough."
"Be prepared for difficult homework sets that test your understanding deeply."
"The problem sets are hard but force you to really learn the material..."

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 Introduction to Probability with these activities:
Follow Khan Academy's 'Probability' playlist
Build a strong foundation in probability
Browse courses on Conditional Probability
Show steps
  • Create a Khan Academy account
  • Locate the 'Probability' playlist under 'Math'
  • Watch all the videos in the playlist
  • Complete the practice exercises and quizzes
Review 'Introduction to Probability' by Blitzstein
Familiarize yourself with core probability concepts
View Introduction to Probability, Second Edition... on Amazon
Show steps
  • Read the first three chapters of the book
  • Annotate and summarize the main concepts covered
  • Complete the end-of-chapter exercises
Form a study group to discuss course material
Engage with peers to clarify concepts and reinforce understanding
Show steps
  • Identify a group of classmates with similar interests
  • Schedule regular meetings
  • Discuss the course material, share insights, and work through problems together
Four other activities
Expand to see all activities and additional details
Show all seven activities
Solve probability problems from Brilliant.org
Reinforce understanding of probability concepts through practice
Browse courses on Probability Distributions
Show steps
  • Sign up for a Brilliant.org account
  • Navigate to the 'Probability' section
  • Complete at least 10 problems in each subsection
  • Review your solutions and identify areas for improvement
Develop a cheat sheet on probability distributions
Summarize key concepts to enhance understanding and retention
Browse courses on Probability Distributions
Show steps
  • Identify the most important probability distributions covered in the course
  • Gather information about each distribution (e.g., formula, parameters, properties)
  • Create a visually appealing cheat sheet
  • Review the cheat sheet regularly
Tutor other students in probability
Deepen understanding by explaining concepts to others
Browse courses on Probability
Show steps
  • Identify students who are struggling with the material
  • Offer your assistance and schedule tutoring sessions
  • Review the course concepts and work through problems together
  • Provide feedback and encouragement
Participate in the 'Chance' magazine's student essay contest
Test your understanding and communication skills
Show steps
  • Read the contest guidelines and submission requirements
  • Brainstorm and develop a topic
  • Research and write a compelling essay
  • Proofread and edit your essay carefully

Career center

Learners who complete Introduction to Probability will develop knowledge and skills that may be useful to these careers:
Data Scientist
A Data Scientist is responsible for collecting, cleaning, and analyzing data. They build machine learning models, identify trends and patterns, and help businesses make informed decisions. This course in Introduction to Probability is a great starting point for those looking to get into the field of data science. It provides a solid foundation in the fundamentals of probability, which is essential for understanding data and making accurate predictions.
See salaries and explore the career path for Data Scientist
Statistician
Statisticians collect, analyze, interpret, and present data. They work in a variety of industries, including healthcare, finance, and marketing. This course in Introduction to Probability provides a solid foundation in the fundamentals of probability, which is essential for a successful career as a statistician. The course covers topics such as probability distributions, hypothesis testing, and regression analysis.
See salaries and explore the career path for Statistician
Quantitative Analyst
Quantitative Analysts, also known as Quants, use mathematical and statistical models to analyze financial data and make investment decisions. They work for hedge funds, investment banks, and other financial institutions. This course in Introduction to Probability provides a solid foundation in the fundamentals of probability, which is essential for a successful career as a Quant. The course covers topics such as probability distributions, stochastic processes, and financial modeling.
See salaries and explore the career path for Quantitative Analyst
Risk Manager
Risk Managers identify, assess, and manage risks. They work in a variety of industries, including finance, healthcare, and insurance. This course in Introduction to Probability provides a solid foundation in the fundamentals of probability, which is essential for a successful career as a Risk Manager. The course covers topics such as probability distributions, risk assessment, and decision making under uncertainty.
See salaries and explore the career path for Risk Manager
Actuary
Actuaries use mathematical and statistical models to assess risk and uncertainty. They work in the insurance industry, helping to set premiums and design insurance policies. This course in Introduction to Probability provides a solid foundation in the fundamentals of probability, which is essential for a successful career as an Actuary. The course covers topics such as probability distributions, risk assessment, and financial modeling.
See salaries and explore the career path for Actuary
Software Engineer
Software Engineers design, develop, and maintain software applications. This course in Introduction to Probability provides a solid foundation in the fundamentals of probability, which is essential for a successful career as a Software Engineer. The course covers topics such as probability distributions, algorithms, and data structures.
See salaries and explore the career path for Software Engineer
Data Analyst
Data Analysts collect, clean, and analyze data. They work in a variety of industries, including healthcare, finance, and marketing. This course in Introduction to Probability provides a solid foundation in the fundamentals of probability, which is essential for a successful career as a Data Analyst. The course covers topics such as probability distributions, hypothesis testing, and regression analysis.
See salaries and explore the career path for Data Analyst
Business Analyst
Business Analysts help businesses make informed decisions by analyzing data and identifying trends. This course in Introduction to Probability provides a solid foundation in the fundamentals of probability, which is essential for a successful career as a Business Analyst. The course covers topics such as probability distributions, hypothesis testing, and regression analysis.
See salaries and explore the career path for Business Analyst
Financial Analyst
Financial Analysts analyze financial data to make investment recommendations. They work for investment banks, hedge funds, and other financial institutions. This course in Introduction to Probability provides a solid foundation in the fundamentals of probability, which is essential for a successful career as a Financial Analyst. The course covers topics such as probability distributions, risk assessment, and financial modeling.
See salaries and explore the career path for Financial Analyst
Market Researcher
Market Researchers collect and analyze data to understand consumer behavior. They work for a variety of organizations, including marketing agencies, product development firms, and consulting companies. This course in Introduction to Probability provides a solid foundation in the fundamentals of probability, which is essential for a successful career as a Market Researcher. The course covers topics such as probability distributions, hypothesis testing, and regression analysis.
See salaries and explore the career path for Market Researcher
Operations Research Analyst
Operations Research Analysts use mathematical and statistical models to improve the efficiency of business operations. They work in a variety of industries, including manufacturing, transportation, and healthcare. This course in Introduction to Probability provides a solid foundation in the fundamentals of probability, which is essential for a successful career as an Operations Research Analyst. The course covers topics such as probability distributions, optimization, and simulation.
See salaries and explore the career path for Operations Research Analyst
Product Manager
Product Managers are responsible for the development and launch of new products. They work in a variety of industries, including technology, consumer goods, and healthcare. This course in Introduction to Probability may be useful for those who want to get into product management. The course covers topics such as probability distributions, hypothesis testing, and regression analysis, which can be helpful for understanding customer behavior and making data-driven decisions.
See salaries and explore the career path for Product Manager
Project Manager
Project Managers are responsible for planning, executing, and closing projects. They work in a variety of industries, including construction, IT, and healthcare. This course in Introduction to Probability may be useful for those who want to get into project management. The course covers topics such as probability distributions, risk assessment, and decision making under uncertainty, which can be helpful for managing projects and making data-driven decisions.
See salaries and explore the career path for Project Manager
Consultant
Consultants provide advice to businesses and organizations on a variety of topics. This course in Introduction to Probability may be useful for those who want to get into consulting. The course covers topics such as probability distributions, hypothesis testing, and regression analysis, which can be helpful for analyzing data and making recommendations.
See salaries and explore the career path for Consultant
Teacher
Teachers educate students at all levels, from elementary school to college. This course in Introduction to Probability may be useful for those who want to get into teaching. The course covers topics such as probability distributions, hypothesis testing, and regression analysis, which can be helpful for understanding student learning and making data-driven decisions.
See salaries and explore the career path for Teacher

Reading list

We've selected 11 books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Introduction to Probability.
Cover image
Introduction to Probability, Second Edition
Save
Is the official textbook for the course and provides a detailed and rigorous introduction to probability. It covers a wide range of topics, from basic concepts to advanced techniques.
Introduction to Probability, Second Edition...
Hardcover
$$$
Introduction to Probability, Second Edition...
Kindle Edition
$$$
Cover image
Statistical Inference
Save
Provides a comprehensive introduction to statistical inference, with a focus on the development of statistical models. It is written in a rigorous and mathematical style and is suitable for students with a strong background in mathematics.
Statistical Inference (Chapman & Hall/CRC Texts in...
Hardcover
$$$
Statistical Inference
Hardcover
$$$
Statistical Inference
Hardcover
$$$
Times Higher Education Abroad excellent selection...
Paperback
$$
Statistical Inference (Chapman & Hall/CRC Texts in...
Kindle Edition
$$$
Statistical Inference
Kindle Edition
$$$
Cover image
All of Statistics
Save
Provides a comprehensive overview of statistical inference, with a focus on the development of statistical models. It is written in a clear and concise style and is suitable for students with a strong background in mathematics.
All of Statistics: A Concise Course in Statistical...
Hardcover
$$
All of Nonparametric Statistics (Springer Texts in...
Hardcover
$$$$
All of statistics : A concise course in statistic...
Kindle Edition
$
Cover image
Probability
Save
Provides a comprehensive introduction to probability theory, with a focus on the development of mathematical models. It is written in a rigorous and mathematical style and is suitable for students with a strong background in mathematics.
Probability
Paperback
Check
Probability
Kindle Edition
Check
Cover image
Real Analysis and Probability
Save
Provides a comprehensive introduction to real analysis and probability theory, with a focus on the development of mathematical models. It is written in a rigorous and mathematical style and is suitable for students with a strong background in mathematics.
Real Analysis and Probability
Paperback
Check
Real Analysis and Probability
Kindle Edition
Check
Cover image
Counterexamples in Measure and Integration
Save
Provides a comprehensive introduction to measure theory and probability theory, with a focus on the development of mathematical models. It is written in a rigorous and mathematical style and is suitable for students with a strong background in mathematics.
Counterexamples in Measure and Integration
Kindle Edition
$$$
An Introduction to Probability Theory and Its...
Save
Provides a comprehensive introduction to probability theory and its applications, with a focus on the development of mathematical models. It is written in a rigorous and mathematical style and is suitable for students with a strong background in mathematics.
An Introduction to Probability Theory and Its...
Paperback
Check
An Introduction to Probability Theory and Its...
Kindle Edition
Check
Cover image
Probability and Measure
Save
Provides a comprehensive introduction to probability and measure theory, with a focus on the development of mathematical models. It is written in a rigorous and mathematical style and is suitable for students with a strong background in mathematics.
Probability and Measure
Hardcover
$$$$
Probability and Measure
Hardcover
$$$$
Convergence of Probability Measures
Hardcover
$$$$
Probability and Measure (Wiley Series in...
Kindle Edition
$$$$
Convergence of Probability Measures (Wiley Series...
Kindle Edition
$$$$
Cover image
Monte Carlo Statistical Methods
Save
Provides a comprehensive introduction to Monte Carlo statistical methods, with a focus on applications in science and engineering. It is written in a clear and concise style and is suitable for students with a strong background in mathematics.
Monte Carlo Statistical Methods (Springer Texts in...
Hardcover
$$$
Cover image
Introduction to Stochastic Processes
Save
Provides a comprehensive introduction to stochastic processes, with a focus on applications in science and engineering. It is written in a clear and concise style and is suitable for students with a strong background in mathematics.
Introduction to Stochastic Processes (Chapman &...
Hardcover
$$$
Introduction to Stochastic Processes (Chapman &...
Kindle Edition
$$$
Cover image
Probability and Random Processes
Save
Provides a comprehensive introduction to probability and random processes, with a focus on applications in science and engineering. It is written in a clear and concise style and is suitable for students with a strong background in mathematics.
Probability and Random Processes: Fourth Edition
Hardcover
$$$$

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Course image
Rating
5.0 Filled star Filled star Filled star Filled star Filled star
Effort
5 to 10 hours per week for 10 weeks
Level
Intermediate
Via
edX
Institution
Harvard University
Instructor
Joseph Blitzstein
Language
English
Transcripts
Español Français Português Deutsch 中文 العربية हिंदी Türkçe తెలుగు Bahasa Indonesia Kiswahili
Traffic lights
Read about what's good
what should give you pause
and possible dealbreakers
Explores probability and statistics in a practical way, providing real-world examples from fields like medicine and sports
Taught by Joseph Blitzstein, a recognized expert in probability and data science
Develops a strong foundation in probability for further study in statistical inference and other related fields
Suitable for beginners who want to build a solid foundation in probability and statistics
May require additional knowledge in mathematics, particularly calculus, for some sections
The course does not cover advanced topics in probability and statistics
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