# 2020/2021

## Content, progress and pedagogy of the module

After attending the course the students have developed the engineering intuition of the fundamental concepts and results of Probability, Statistics, and Stochastic Processes. They are able to apply the taught material to model and solve simple engineering problems involving randomness.

### Learning objectives

#### Knowledge

• Must have knowledge about the concept of probability spaces
• Must have knowledge about the conceptual models of estimation and hypothesis testing
• Must be able to understand the basic concepts of probability theory:
• Probability of events
• Random variables
• Must be able to understand the basic concepts of statistics:
• Binary hypothesis testing.

#### Skills

• Must be able to apply/compute
• Bayes rule in simple contexts
• The probability that Binomial, Poisson, and Gaussian random variables take values in a specified interval
• The mean and variance of Binomial, Poisson, and Gaussian random variables
• The marginal distributions of multi-variate Gaussian variables
• Must be able to apply and interpret
• ML-estimation in simple contexts involving the Binomial, Poisson, and Gaussian distribution
• Binary-hypothesis tests in simple contexts involving the Binomial, Poisson, and Gaussian distribution

#### Competences

• Must be able to apply the general concepts of Probability Theory and Statistics in a new simple context. This includes choosing the suitable methods, evaluating the outcomes, and drawing the appropriate conclusions.

### Type of instruction

Combination of e.g. face-to-face lectures, exercises, self-studies and mini-projects (using e.g. MATLAB).

## Exam

### Exams

 Name of exam Introduction to Probability Theory and Statistics Type of exam Written or oral exam ECTS 5 Assessment 7-point grading scale Type of grading Internal examination Criteria of assessment The criteria of assessment are stated in the Examination Policies and Procedures