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This course provides an introduction to probability theory. You will encounter discrete and continuous random variables and learn in which situations they appear, what their properties are and how they interact.

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 course
This 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 You'll Learn

• 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.

Course 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)
• applications

Week 6: Simulation

• Monte Carlo simulation
• examples