Syllabus for Probability Theory and Statistical Inference I

Sannolikhetslära och inferensteori I


  • 7.5 credits
  • Course code: 2ST065
  • Education cycle: First cycle
  • Main field(s) of study and in-depth level: Statistics G1F

    Explanation of codes

    The code indicates the education cycle and in-depth level of the course in relation to other courses within the same main field of study according to the requirements for general degrees:

    First cycle

    • G1N: has only upper-secondary level entry requirements
    • G1F: has less than 60 credits in first-cycle course/s as entry requirements
    • G1E: contains specially designed degree project for Higher Education Diploma
    • G2F: has at least 60 credits in first-cycle course/s as entry requirements
    • G2E: has at least 60 credits in first-cycle course/s as entry requirements, contains degree project for Bachelor of Arts/Bachelor of Science
    • GXX: in-depth level of the course cannot be classified

    Second cycle

    • A1N: has only first-cycle course/s as entry requirements
    • A1F: has second-cycle course/s as entry requirements
    • A1E: contains degree project for Master of Arts/Master of Science (60 credits)
    • A2E: contains degree project for Master of Arts/Master of Science (120 credits)
    • AXX: in-depth level of the course cannot be classified

  • Grading system: Fail (U), Pass (G), Pass with distinction (VG)
  • Established: 2007-01-24
  • Established by:
  • Revised: 2021-09-10
  • Revised by: The Department Board
  • Applies from: Spring 2022
  • Entry requirements:

    At least 15 credits from Statistics A, 30 credits

  • 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


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.


Lectures ( 6-10 hours a week).


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.

"If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the University's disability coordinator."

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.

Reading list

Reading list

Applies from: Spring 2022

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