Syllabus for Probability Theory and Statistical Inference I

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.