Probability Theory from edX

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.

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

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

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

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

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Apply the skills you learned in the Calculus courses of this series.

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Review the definitions of derivatives and integrals.
Practice finding derivatives and integrals of simple functions.

Join a study group with other students

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Collaborate with other students to learn and understand probability theory concepts more effectively.

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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

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Reinforce your understanding of probability theory by solving practice problems.

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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

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Create a cheat sheet of probability formulas

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Summarize the key formulas and concepts of probability theory in a concise and accessible format.

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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

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Expand your knowledge of probability theory by exploring advanced topics through guided tutorials.

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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

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Apply the principles of probability theory to solve a real-world problem through simulation modeling.

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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

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Showcase your skills in probability theory by building a portfolio of projects.

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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

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Connect with other probability theory enthusiasts and learn about the latest developments in the field.

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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

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.

See salaries and explore the career path for Actuary

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.

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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.

See salaries and explore the career path for Data 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.

See salaries and explore the career path for Financial 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.

See salaries and explore the career path for Risk 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.

See salaries and explore the career path for Quantitative 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.

See salaries and explore the career path for Operations Research Analyst

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.

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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.

See salaries and explore the career path for Machine Learning Engineer

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.

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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.

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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.

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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.

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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.

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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.

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