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Christophe Smet,
Tom Vroegrijk,
and
Annoesjka Cabo
A strong foundation in mathematics is critical for success in all science and engineering disciplines. Whether you want to make a strong start to a master’s degree, prepare for more advanced courses, solidify your knowledge in a professional context or simply brush up on fundamentals, this course will get you up to speed.
Probability theory can be applied to learn more about real-life problems, and it is useful for building models. Moreover, it provides the basis for statistics and applications in data analysis. Therefore, it is a useful subject for any aspiring or practicing engineer.
Read more
A strong foundation in mathematics is critical for success in all science and engineering disciplines. Whether you want to make a strong start to a master’s degree, prepare for more advanced courses, solidify your knowledge in a professional context or simply brush up on fundamentals, this course will get you up to speed.
Probability theory can be applied to learn more about real-life problems, and it is useful for building models. Moreover, it provides the basis for statistics and applications in data analysis. Therefore, it is a useful subject for any aspiring or practicing engineer.
Read more
A strong foundation in mathematics is critical for success in all science and engineering disciplines. Whether you want to make a strong start to a master’s degree, prepare for more advanced courses, solidify your knowledge in a professional context or simply brush up on fundamentals, this course will get you up to speed.
Probability theory can be applied to learn more about real-life problems, and it is useful for building models. Moreover, it provides the basis for statistics and applications in data analysis. Therefore, it is a useful subject for any aspiring or practicing engineer.
We will use some basic calculus, in particular (partial) differentiation and (multiple) integration. The focus will be on the interpretation rather than on the computation; so the required techniques will be low-level. If, however, you feel insecure about these topics, you can brush up on them in our calculus courses within this series.
This course will offer you an overview of the probability theory elements common to most engineering bachelor programs. It will provide enough depth to cover the probability theory you need to succeed in your engineering master’s or profession in areas such as modeling, finance, signal processing, logistics and more.
This is a review courseThis self-contained course is modular, so you do not need to follow the entire course if you wish to focus on a particular aspect. As a review course you are expected to have previously studied or be familiar with most of the material. Hence the pace will be higher than in an introductory course.
This format is ideal for refreshing your bachelor level mathematics and letting you practice as much as you want. Through the Grasple platform, you will have access to plenty of exercises and receive intelligent, personal and immediate feedback.
Register for this course and see more details by visiting:
OpenCourser.com/course/7l6m93/probability
What's inside
Learning objectives
- Describe discrete and continuous random variables (rvs).
- Deduce properties of rvs, such as expectation and variance.
- Gain insight into when certain rvs appear in a specific context.
- Observe how two rvs interact.
- Obtain understanding into some limiting results, in particular the central limit theorem and how powerful it is.
- Simulate some real-life situations.
- Describe discrete and continuous random variables (rvs).
- Deduce properties of rvs, such as expectation and variance.
- Gain insight into when certain rvs appear in a specific context.
- Observe how two rvs interact.
- Obtain understanding into some limiting results, in particular the central limit theorem and how powerful it is.
- Simulate some real-life situations.
Syllabus
Week 1: Probability spaces and general concepts
events
probability function
conditional probability
Read more
Syllabus
Week 1: Probability spaces and general concepts
events
probability function
conditional probability
Read more
introduction to discrete random variables
Week 2: Discrete random variables
Bernoulli distribution
geometric distribution
binomial distribution
Poisson distribution
applications
Week 3: Continuous random variables
density function
exponential distribution
Pareto distribution
normal distribution
Week 4: Multivariate random variables
joint distribution
marginal distribution
covariance and correlation
independence
conditional expectation
Week 5: Limiting theorems
law of large numbers (LLN)
central limit theorem (CLT)
Week 6: Simulation
Monte Carlo simulation
examples
Good to know
Good to know
Know what's good ,
what to watch for , and
possible dealbreakers
Requires a strong foundation in calculus and probability theory
Covers essential probability theory elements for engineering applications
Emphasizes interpretation over computation, making it accessible even for learners with limited calculus skills
Provides ample practice opportunities through the Grasple platform
Suitable for both review and foundational learning
Assumes familiarity with most of the material, making it less suitable for absolute beginners
Save this course
Save Probability Theory to your list so you can find it easily later:
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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 with these
activities:
Review derivatives and integrals
Show steps
Apply the skills you learned in the Calculus courses of this series.
Browse courses on
Calculus
Show steps
-
Review the definitions of derivatives and integrals.
-
Practice finding derivatives and integrals of simple functions.
Join a study group with other students
Show steps
Collaborate with other students to learn and understand probability theory concepts more effectively.
Browse courses on
Probability Theory
Show steps
-
Find other students who are interested in forming a study group.
-
Decide on a meeting time and location.
-
Prepare for each meeting by reviewing the course material and completing any assigned problems.
-
Meet with the group and discuss the course material.
-
Work together on practice problems and assignments.
Solve probability theory problems
Show steps
Reinforce your understanding of probability theory by solving practice problems.
Browse courses on
Probability Theory
Show steps
-
Find the probability of events.
-
Calculate the expected value and variance of random variables.
-
Use probability distributions to model real-world phenomena.
Five other activities
Expand to see all activities and additional details
Show all eight activities
Create a cheat sheet of probability formulas
Show steps
Summarize the key formulas and concepts of probability theory in a concise and accessible format.
Browse courses on
Probability Theory
Show steps
-
Gather the most important formulas and concepts from the course materials.
-
Organize the formulas and concepts in a logical and easy-to-understand way.
-
Create a visually appealing and user-friendly cheat sheet.
Follow tutorials on advanced probability theory topics
Show steps
Expand your knowledge of probability theory by exploring advanced topics through guided tutorials.
Browse courses on
Probability Theory
Show steps
-
Identify areas of probability theory that you want to learn more about.
-
Find high-quality tutorials that cover these topics in depth.
-
Follow the tutorials carefully and complete the associated exercises.
Develop a simulation model to solve a real-world problem
Show steps
Apply the principles of probability theory to solve a real-world problem through simulation modeling.
Browse courses on
Probability Theory
Show steps
-
Identify a problem that can be solved using simulation modeling.
-
Develop a simulation model that represents the problem.
-
Run the simulation model and analyze the results.
-
Use the results of the simulation to make recommendations for solving the problem.
Build a portfolio of probability theory projects
Show steps
Showcase your skills in probability theory by building a portfolio of projects.
Browse courses on
Probability Theory
Show steps
-
Identify different types of probability theory projects that you can work on.
-
Choose a project that interests you and that will challenge you.
-
Develop a plan for completing the project.
-
Execute your plan and complete the project.
-
Document your work and add the project to your portfolio.
Attend a probability theory conference or workshop
Show steps
Connect with other probability theory enthusiasts and learn about the latest developments in the field.
Browse courses on
Probability Theory
Show steps
-
Find a probability theory conference or workshop that interests you.
-
Register for the event and make travel arrangements.
-
Attend the event and participate in the activities.
Review derivatives and integrals
Show steps
Apply the skills you learned in the Calculus courses of this series.
Browse courses on
Calculus
Show steps
Show steps
Show steps
- Review the definitions of derivatives and integrals.
- Practice finding derivatives and integrals of simple functions.
Join a study group with other students
Show steps
Collaborate with other students to learn and understand probability theory concepts more effectively.
Browse courses on
Probability Theory
Show steps
Show steps
Show steps
- Find other students who are interested in forming a study group.
- Decide on a meeting time and location.
- Prepare for each meeting by reviewing the course material and completing any assigned problems.
- Meet with the group and discuss the course material.
- Work together on practice problems and assignments.
Solve probability theory problems
Show steps
Reinforce your understanding of probability theory by solving practice problems.
Browse courses on
Probability Theory
Show steps
Show steps
Show steps
- Find the probability of events.
- Calculate the expected value and variance of random variables.
- Use probability distributions to model real-world phenomena.
Five other activities
Expand to see all activities and additional details
Show all eight activities
Create a cheat sheet of probability formulas
Show steps
Summarize the key formulas and concepts of probability theory in a concise and accessible format.
Browse courses on
Probability Theory
Show steps
Show steps
Show steps
- Gather the most important formulas and concepts from the course materials.
- Organize the formulas and concepts in a logical and easy-to-understand way.
- Create a visually appealing and user-friendly cheat sheet.
Follow tutorials on advanced probability theory topics
Show steps
Expand your knowledge of probability theory by exploring advanced topics through guided tutorials.
Browse courses on
Probability Theory
Show steps
Show steps
Show steps
- Identify areas of probability theory that you want to learn more about.
- Find high-quality tutorials that cover these topics in depth.
- Follow the tutorials carefully and complete the associated exercises.
Develop a simulation model to solve a real-world problem
Show steps
Apply the principles of probability theory to solve a real-world problem through simulation modeling.
Browse courses on
Probability Theory
Show steps
Show steps
Show steps
- Identify a problem that can be solved using simulation modeling.
- Develop a simulation model that represents the problem.
- Run the simulation model and analyze the results.
- Use the results of the simulation to make recommendations for solving the problem.
Build a portfolio of probability theory projects
Show steps
Showcase your skills in probability theory by building a portfolio of projects.
Browse courses on
Probability Theory
Show steps
Show steps
Show steps
- Identify different types of probability theory projects that you can work on.
- Choose a project that interests you and that will challenge you.
- Develop a plan for completing the project.
- Execute your plan and complete the project.
- Document your work and add the project to your portfolio.
Attend a probability theory conference or workshop
Show steps
Connect with other probability theory enthusiasts and learn about the latest developments in the field.
Browse courses on
Probability Theory
Show steps
Show steps
Show steps
- Find a probability theory conference or workshop that interests you.
- Register for the event and make travel arrangements.
- Attend the event and participate in the activities.
Career center
Learners who complete Probability Theory will develop knowledge and skills
that may be useful to these careers:
Actuary
Actuary
Actuaries use mathematical and statistical skills to assess risk and uncertainty. They work in a variety of industries, including insurance, finance, and consulting. The Probability Theory course can help you build a strong foundation in the mathematical and statistical concepts that are essential for success in this field. The course covers topics such as probability spaces, random variables, and limiting theorems, which are all important for understanding and modeling risk and uncertainty.
Market Researcher
Market Researcher
Market researchers use data to understand consumer behavior. They work in a variety of industries, including marketing, advertising, and product development. The Probability Theory course can help you build a strong foundation in the statistical concepts that are essential for success in this field. The course covers topics such as probability distributions, hypothesis testing, and regression analysis, which are all important for understanding and analyzing market research data.
Data Analyst
Data Analyst
Data analysts use data to solve business problems. They work in a variety of industries, including technology, finance, and healthcare. The Probability Theory course can help you build a strong foundation in the statistical concepts that are essential for success in this field. The course covers topics such as probability distributions, hypothesis testing, and regression analysis, which are all important for understanding and analyzing data.
Financial Analyst
Financial Analyst
Financial analysts use financial data to make investment recommendations. They work in a variety of industries, including investment banks, asset management firms, and hedge funds. The Probability Theory course can help you build a strong foundation in the statistical concepts that are essential for success in this field. The course covers topics such as probability distributions, hypothesis testing, and regression analysis, which are all important for understanding and analyzing financial data.
Risk Analyst
Risk Analyst
Risk analysts use mathematical and statistical techniques to assess risk and uncertainty. They work in a variety of industries, including insurance, finance, and consulting. The Probability Theory course can help you build a strong foundation in the mathematical and statistical concepts that are essential for success in this field. The course covers topics such as probability spaces, random variables, and limiting theorems, which are all important for understanding and modeling risk and uncertainty.
Quantitative Analyst
Quantitative Analyst
Quantitative analysts use mathematical and statistical models to make investment decisions. They work in a variety of industries, including investment banks, asset management firms, and hedge funds. The Probability Theory course can help you build a strong foundation in the mathematical and statistical concepts that are essential for success in this field. The course covers topics such as probability spaces, random variables, and stochastic processes, which are all important for understanding and modeling financial data.
Operations Research Analyst
Operations Research Analyst
Operations research analysts use mathematical and statistical techniques to improve the efficiency of business operations. They work in a variety of industries, including manufacturing, logistics, and healthcare. The Probability Theory course can help you build a strong foundation in the mathematical and statistical concepts that are essential for success in this field. The course covers topics such as probability spaces, random variables, and optimization, which are all important for understanding and modeling business operations.
Statistician
Statistician
Statisticians use mathematical and statistical techniques to collect, analyze, and interpret data. They work in a variety of industries, including healthcare, education, and government. The Probability Theory course can help you build a strong foundation in the mathematical and statistical concepts that are essential for success in this field. The course covers topics such as probability distributions, hypothesis testing, and regression analysis, which are all important for understanding and analyzing data.
Machine Learning Engineer
Machine Learning Engineer
Machine learning engineers use mathematical and statistical techniques to develop machine learning models. They work in a variety of industries, including technology, finance, and healthcare. The Probability Theory course can help you build a strong foundation in the mathematical and statistical concepts that are essential for success in this field. The course covers topics such as probability distributions, hypothesis testing, and machine learning, which are all important for understanding and developing machine learning models.
Data Scientist
Data Scientist
Data scientists use mathematical and statistical techniques to extract insights from data. They work in a variety of industries, including technology, finance, and healthcare. The Probability Theory course can help you build a strong foundation in the mathematical and statistical concepts that are essential for success in this field. The course covers topics such as probability distributions, hypothesis testing, and machine learning, which are all important for understanding and analyzing data.
Software Engineer
Software Engineer
Software engineers design, develop, and maintain software systems. They work in a variety of industries, including technology, finance, and healthcare. The Probability Theory course may be useful for software engineers who want to develop software systems that are reliable and efficient. The course covers topics such as probability spaces, random variables, and limiting theorems, which are all important for understanding and modeling software systems.
Systems Analyst
Systems Analyst
Systems analysts design, develop, and maintain computer systems. They work in a variety of industries, including technology, finance, and healthcare. The Probability Theory course may be useful for systems analysts who want to develop computer systems that are reliable and efficient. The course covers topics such as probability spaces, random variables, and limiting theorems, which are all important for understanding and modeling computer systems.
Project Manager
Project Manager
Project managers plan, execute, and close projects. They work in a variety of industries, including technology, finance, and healthcare. The Probability Theory course may be useful for project managers who want to manage projects more effectively. The course covers topics such as probability spaces, random variables, and limiting theorems, which are all important for understanding and managing project risks.
Business Analyst
Business Analyst
Business analysts use data to solve business problems. They work in a variety of industries, including technology, finance, and healthcare. The Probability Theory course may be useful for business analysts who want to use data to make better decisions. The course covers topics such as probability distributions, hypothesis testing, and regression analysis, which are all important for understanding and analyzing data.
Teacher
Teacher
Teachers plan, execute, and close lessons. They work in a variety of educational settings, including schools, colleges, and universities. The Probability Theory course may be useful for teachers who want to teach mathematics and statistics more effectively. The course covers topics such as probability spaces, random variables, and limiting theorems, which are all important for understanding and teaching mathematics and statistics.
For more career information including salaries, visit:
OpenCourser.com/course/7l6m93/probability
Reading list
We've selected 13 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
Probability Theory.
Save
Offers a comprehensive introduction to probability theory, covering both discrete and continuous random variables, as well as limit theorems. It is written in a clear and concise style and provides plenty of exercises to help the reader understand the material. It's a great reference for anyone who wants to learn more about probability theory.
This undergraduate textbook provides an overview of probability theory, with a focus on the applications of probability in real-world problems. It covers a wide range of topics, including discrete and continuous random variables, joint distributions, and limit theorems. It is written in a clear and engaging style and is suitable for students with a basic understanding of calculus.
This textbook covers information theory, inference, and learning algorithms, with a focus on providing a comprehensive overview of the subject. It is written in a clear and concise style and provides plenty of exercises to help the reader understand the material.
This textbook good introduction to probability theory, covering both discrete and continuous random variables. It is written in a clear and concise style and provides plenty of exercises to help the reader understand the material. It's an excellent resource for anyone who wants to learn the basics of probability theory.
This textbook covers statistical inference, with a focus on data science. It is written in a clear and concise style and provides plenty of exercises to help the reader understand the material.
This textbook covers Bayesian data analysis, with a focus on applications in a variety of fields. It is written in a clear and concise style and provides plenty of exercises to help the reader understand the material.
This textbook covers machine learning, with a focus on providing a probabilistic perspective on the subject. It is written in a clear and concise style and provides plenty of exercises to help the reader understand the material.
This textbook covers probability theory and statistics, with a focus on applications in engineering and science. It is written in a clear and concise style and provides plenty of exercises to help the reader understand the material.
This textbook covers probability theory, with a focus on applications in data science. It is written in a clear and concise style and provides plenty of exercises to help the reader understand the material. It's a great resource for anyone who wants to learn how to apply probability theory to data science.
Save
This textbook covers probability theory and stochastic processes, with a focus on providing a friendly introduction to the subject. It is written in a clear and engaging style and provides plenty of exercises to help the reader understand the material.
Save
This textbook provides a comprehensive introduction to stochastic processes, covering both continuous-time and discrete-time processes. It is suitable for graduate students and researchers in mathematics, statistics, and engineering.
This textbook covers probability theory and random processes, providing a more advanced treatment than the previous two books. It is suitable for graduate students and researchers in mathematics, statistics, and engineering. It covers a wide range of topics, including measure theory, stochastic processes, and Markov chains.
Save
This textbook covers a wide range of topics in probability theory and mathematical statistics, including measure theory, random variables, and statistical inference. It is suitable for graduate students and researchers in mathematics, statistics, and engineering.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/7l6m93/probability
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Effort
4 to 6 hours per week for 6 weeks
Level
Intermediate
Via
edX
Institution
Delft University of Technology
Instructors
Christophe Smet
Tom Vroegrijk
Annoesjka Cabo
Session
July 3, 2024
- May 28, 2025
Language
English
Transcripts
English
Español
Français
Português
Deutsch
中文
العربية
हिंदी
Türkçe
తెలుగు
Bahasa Indonesia
Kiswahili
Good to know
Requires a strong foundation in calculus and probability theory
Covers essential probability theory elements for engineering applications
Emphasizes interpretation over computation, making it accessible even for learners with limited calculus skills
Provides ample practice opportunities through the Grasple platform
Suitable for both review and foundational learning
Assumes familiarity with most of the material, making it less suitable for absolute beginners
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