SF1901 Probability Theory and Statistics 6.0 credits

Sannolikhetsteori och statistik I

The overall purpose of the course is that the student should be well acquainted with basic concepts, theory, models and solution methods in probability theory and statistical inference.

  • Educational level

    First cycle
  • Academic level (A-D)

  • Subject area

  • Grade scale

    A, B, C, D, E, FX, F

Course offerings

Autumn 16 CENMI, CMETE for programme students

Autumn 16 CINTE for programme students

Autumn 16 CMAST CFATE for programme students

Autumn 16 CINEK for programme students

Autumn 16 TCOMK for programme students

Spring 17 CELTE2CTFYS2 for programme students

Spring 17 CTFYS1CMEDT for programme students

Spring 17 CDATE2 for programme students

Spring 16 CDATE CMEDT for programme students

Intended learning outcomes

To pass the course, the student should be able to do the following:

  • construct elementary statistical models for experiments
  • describe standard models and explain the applicability of the models in given examples
  • define and calculate descriptive quantities like expectation, variance, and percentiles for distributions and data sets.
  • with standard methods calculate estimates of unknown quantities and quantify the uncertainty in these estimates
  • value and compare methods of estimation
  • analyse how measuring accuracy affect conclusions and quantify risks and error probabilities when testing statistical hypothesis

To receive the highest grade, the student should in addition be able to do the following:

  • Combine all the concepts and methods mentioned above in order to solve more complex problems.

Course main content

Basic concepts like probabilities, conditional probabilities and independent events. Discrete and continuous random variables, especially one dimensional random variables. Measures of location, scale and dependency of random variables and data sets. Common distributions and models: normal, binomial and Poisson distribution. Central limit theorem and Law of large numbers.

Descriptive statistics.

Point estimates and general methods of estimation as the method of maximum likelihood and least squares. General confidence intervals but specifically confidence intervals for mean and variance of normally distributed observations. Confidence intervals for proportions, difference in means and proportions.

Testing statistical hypothesis. Chi2-test of distribution, test of homogeneity and contingency. Linear regression.


Basic differential and integral calculus.


Blom et al. Sannolikhetslära och statistikteori med tillämpningar, Studentlitteratur
Complemental material from the department.


  • TEN1 - Examination, 6.0, grade scale: A, B, C, D, E, FX, F

Requirements for final grade

Written examination.

Offered by



Thomas Önskog (onskog@kth.se)


Thomas Önskog <onskog@kth.se>


Course syllabus valid from: Autumn 07.
Examination information valid from: Autumn 07.