SF1900 Probability Theory and Statistics 6.0 credits

Sannolikhetsteori och statistik

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.

  • Education cycle

    First cycle
  • Main field of study

    Technology
  • Grading scale

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

Course offerings

Autumn 19 for programme students

Autumn 18 TCOMK3 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 account for the applicability of the models in given examples
  • efine and calculate descriptive quantities for probability distributions and data sets, such as measures of central tendency, dispersion and dependence
  • using standard methods, such as maximum likelihood estimation and the method of least squares, calculate estimates of unknown quantities and quantify the uncertainty in these estimates by means of for example error propagation and confidence intervals
  • value and compare methods of estimation, for example with respect to bias and efficiency
  • analyse how measuring accuracy affects conclusions and quantify risks and error probabilities in statistical hypothesis testing

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 such as probability, conditional probability and independent events. Discrete and continuous random variables, in particular one dimensional random variables. Measures of central tendency, dispersion and dependence of random variables and data sets. Common distributions and models, such as the normal, binomial and Poisson distributions. The Central limit theorem and the Law of large numbers.

Descriptive statistics.

Point estimates and general methods of estimation, such as maximum likelihood estimation and the method of least squares. General confidence intervals and in particular confidence intervals for the mean and variance of normally distributed data. Confidence intervals for proportions and for difference in means and proportions.
Statistical hypothesis testing. Chi2-tests of goodness of fit, homogeneity and independence. Linear regression.

Eligibility

Basic linear algebra, calculus in one variable,  calculus in several variables.

Only for students enrolled in a bachelor programme in Information and Communication Technology (TCOMK).

Recommended prerequisites

SF1626/SF1686 Calculus in Several Variable, SF1624/SF1684 Algebra and Geometry 

Literature

Blom, Gunnar. Probability and Statistics (1989), Studentlitteratur

Complemental material from the department.

Examination

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

Requirements for final grade

Passed written examination.

Offered by

SCI/Mathematics

Contact

Per Jörgen Säve-Söderbergh (pjss@kth.se)

Examiner

Per Jörgen Säve-Söderbergh <pjss@kth.se>

Supplementary information

Only for students enrolled in a bachelor programme in Information and Communication Technology (TCOMK).

Version

Course syllabus valid from: Autumn 2017.
Examination information valid from: Autumn 2017.