Introduction to Probability Theory and Statistics

2019/2020

Content, progress and pedagogy of the module

The goal of the course is to enable students to develop the engineering intuition of the fundamental concepts and results of probability, statistics, and stochastic processes, and to apply the taught material to model and solve problems relevant to engineers in “ITCOM”.

Learning objectives

Knowledge

  • Must have knowledge about fundamental concepts in probability, including conditional probability and independence.
  • Must have knowledge about discrete and continuous random variables and relevant properties of these.
  • Must have knowledge about various examples of descriptive statistics, e.g. histograms and scatterplots.
  • Must have knowledge about statistical inference, including estimation, confidence intervals and hypothesis testing.
  • Must have knowledge about important statistical models, like linear regression (simple and multiple), analysis of variance, logistic regression and log-linear models (in particular contingency tables).

Skills

  • Must be able to, given specific data, specify a relevant statistical model and account for the assumptions and limitations of the chosen model.
  • Must be able to use relevant software for carrying out the statistical analysis of given data and be able to interpret the results of the analysis.
  • 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 judge the applicability of statistics within own area.
  • Must be capable of performing a critical judgement of the results of a statistical analysis.
  • Must be capable of communicating the results of a statistical analysis to people with no or little background within statistics.

Type of instruction

Lectures in combination with practical exercises and self-study and mini-projects (using, e.g. MATLAB).

Exam

Exams

Name of examIntroduction to Probability Theory and Statistics
Type of exam
Written or oral exam
ECTS5
Assessment7-point grading scale
Type of gradingInternal examination
Criteria of assessmentAs stated in the Joint Programmes Regulations
http:/​/​www.tech.aau.dk/​uddannelse/​Studieadministration/​

Facts about the module

Danish titleIntroduktion til sandsynlighedsregning og statistik
Module codeESNITCOB4K3N
Module typeCourse
Duration1 semester
SemesterSpring
ECTS5
Language of instructionEnglish
Empty-place SchemeYes
Location of the lectureCampus Copenhagen
Responsible for the module

Organisation

Study BoardStudy Board of Electronics and IT
DepartmentDepartment of Electronic Systems
FacultyTechnical Faculty of IT and Design