## Probability Theory

### Full course description

A brain scientist needs to be able to analyse and model high-dimensional data. These abilities rest on a solid understanding of probability theory and statistics. In this course you will learn the foundations of probabilistic modelling and learn how to use random variables to model and interpret brain science experiments. You will learn useful discrete and continuous probability distributions, and examine the concepts of expectation, moments and statistical independence. After completing this course, you will have obtained an overview of commonly seen probability distributions, as well as several statistical procedures. Additionally, you will be able to deal with problems that involve probabilities and measure their outcome. Furthermore, a selected range of applications of the illustrated concepts in the field of brain science are provided throughout the course.

The final assessment for this course is a numerical grade between 0,0 and 10,0.

### Course objectives

- understand the concept of event space and probability of an event using set theory
- understand the concept of random variable, its probabilistic characterization both in discrete and continuous settings with density and mass functions
- understand statistical independence, conditional probability and Bayes theorem
- identify commonly used discrete and continuous distributions
- understand the concept of a random draw from a population and its probabilistic characterization
- understand the concepts of parameter estimation and of hypothesis testing
- work together or assist each other while solving exercises

- J. Huys
- O. D'Huys