Prerequisite/Recommended prerequisite for participation in the module

Fundamentals in linear algebra, calculus, and Fourier theory

Content, progress and pedagogy of the module

Purpose
After attending the course the students have developed the engineering intuition of the fundamental concepts and results of probability, and statistics. 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, i.e., probability of events, random variables, etc.
• Must be able to understand basic concepts of statistics such as 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 suitable methods, evaluating outcomes, and drawing the appropriate conclusions

Type of instruction

The programme is based on a combination of academic, problem-oriented and interdisciplinary approaches and organised based on the following work and evaluation methods that combine skills and reflection: • Lectures • Classroom instruction • Project work • Workshops • Exercises (individually and in groups) • Teacher feedback • Reflection • Portfolio work

Extent and expected workload

Since it is a 5 ECTS course module, the work load is expected to be 150 hours for the student

Exam

Exams

Name of exam	Introduction to Probability Theory and Statistics
Type of exam	Written or oral examination
ECTS	5
Permitted aids	With certain aids, see list below Unless otherwise stated in the course description in Moodle, it is permitted to bring all kinds of (engineering) aids including books, notes and advanced calculators. If the student brings a computer, it is not permitted to have access to the Internet and the teaching materials from Moodle must therefore be down loaded in advance on the computer. It is emphasized that no form of electronic communication must take place.
Assessment	Passed/Not Passed
Type of grading	Internal examination
Criteria of assessment	As stated in the Joint Programme Regulations. http:/​/​www.engineering.aau.dk/​uddannelse/​studieadministration/​