Probability Theory, 6 credits

Main field of study

Course level

Advancement level

Course offered for

• Master´s Programme in Statistics and Data Mining

Entry requirements

A bachelor’s degree in one of the following subjects: statistics, mathematics, applied mathematics, computer science, engineering, or equivalent. Completed courses in calculus, linear algebra, statistics and programming are required. 
Documented knowledge of English equivalent to Engelska B/Engelska 6. 

Intended learning outcomes

After completetion of the course, the students shall on an advanced level be able to 
- account for major univariate and multivariate probability distributions
- compute different statistics for a given distribution
- derive probability distributions of functions of random vectors, 
- use transforms to compute moments and limit distributions.

Course content

The course aims at enabling insightful modelling of random phenomena and assessment of the probabilistic basis of widely used statistical methods. The course comprises:
- conventional probability distributions,
- expected value, variance, moments,
- joint distribution, conditional distribution, independence,
- the elements of Bayesian approach,
- transforms,
- order statistics,
- multivariate normal distribution,
- types of convergence and theorems related to convergence concept. 

Teaching and working methods

The course consists of lectures and exercise sessions. The lectures are devoted to presentations of theories, concepts and methods. Mathematically oriented problems are solved in the exercise sessions. 
Homework and independent study are a necessary complement to the course. Language of instruction: English. 

Examination

Written examination.
Detailed information about the examination can be found in the course’s study guide. 

Students failing an exam covering either the entire course or part of the course twice are entitled to have a new examiner appointed for the reexamination.

Students who have passed an examination may not retake it in order to improve their grades.

Grades

Other information

Planning and implementation of a course must take its starting point in the wording of the syllabus. The course evaluation included in each course must therefore take up the question how well the course agrees with the syllabus. 

The course is carried out in such a way that both men´s and women´s experience and knowledge is made visible and developed.

Department