# Syllabus for Probability Theory and Statistical Inference I

Sannolikhetslära och inferensteori I

A revised version of the syllabus is available.

## Syllabus

• 7.5 credits
• Course code: 2ST065
• Education cycle: First cycle
• Main field(s) of study and in-depth level: Statistics G1F
• Grading system: Fail (U), Pass (G), Pass with distinction (VG)
• Established: 2007-01-24
• Established by: The Faculty Board of Social Sciences
• Revised: 2010-12-17
• Revised by: The Department Board
• Applies from: Autumn 2011
• Entry requirements:

Statistics A or the equivalent

• Responsible department: Department of Statistics

## Learning outcomes

A student that has completed the course should

? have obtained sufficient knowledge in probability theory that in general principles for inference to be able to understand and apply statistical methods.

? have demonstrated ability to understanding and to use the independently theoretical concepts that occur in the basic theory of applied statistical methods

? have knowledge of how statistical methods can be evaluated by means of computer simulations

? have knowledge about the mathematical methods that are used in theoretical statistics

? be able to assess the prerequisites for a statistical method are satisfied

## Content

Calculus: Limits, differentiation and integration

Probability: Discrete and continuous random variables. The expectation and the variance as operators. Linear combinations of random variables. Bivariate distributions. Conditional expectation and variande. Conditional and Marginal distributions. Sampling distributions, and the central limit theorem.

Inference theory: Point and interval estimation. The maximum likelihood method andlast-squares estimation methods. The properties of estimators: unbiasedness, consistency, relative efficiency. Hypothesis test. The power function.

## Instruction

Lectures ( 6-10 hours a week).

## Assessment

The examination comprises a written test at the end of the course and compulsory assignments, (laboratory sessions). Three grades are awarded for the course: not passed, passed, and passed with distinction.

## Other directives

The course can be included in the Economy programme, the Finsamprogrammet, the Master of Political Sciences programme and the Social scientist programme. The course is compulsory in the Finsamprogrammet with financial specialisation.

The course can also be read as separate course.

## Syllabus Revisions

Applies from: Autumn 2020

Some titles may be available electronically through the University library.

• Devore, Jay L.; Berk, Kenneth N. Modern mathematical statistics with applications

2. ed.: New York, NY [u.a.]: Springer, 2012

Find in the library