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

### Choose semester and course offering

Choose semester and course offering to see information from the correct course syllabus and course offering.

## Content and learning outcomes

### Course contents

• Kolmogorov axioms and basic notions of measurability
• Random variables and their distributions, independence, conditional probabilities, conditional expectation
• Convergence of random variables, law of large numbers
• Convergence in distribution, characteristic function, central limit theorem
• Multivariate normal distribution and introduction to Gaussian processes

### Intended learning outcomes

The overall aim of the course is for students to become well-acquainted with basic probability theory concepts, models and solutions methods applied to concrete problem.

After passing the course, the students should be able to

• formulate and explain central definitions, results and theorems within probability theory
• systematically apply concepts and methods to independently solve basic problems within probability theory
• read and understand a mathematical text.

### Course Disposition

No information inserted

## Literature and preparations

### Specific prerequisites

Completed basic coursein probability theory and statistic (SF1918, SF1922 or equivalent).

### Recommended prerequisites

• Basic course in Multivariable Calculus (SF1626, SF1674 or equivalent)
• Basic course in Algebra and Geometry (SF1624 or equivalent)

### Equipment

No information inserted

### Literature

Announced no later than 4 weeks before the start of the course on the course web page.

## Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

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

### Examination

• TEN1 - Examination, 7,5 hp, betygsskala: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

### Opportunity to raise an approved grade via renewed examination

Due to the current situation, no opportunity to raise an approved grade is presently offered.

### Ethical approach

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

## Further information

### Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web SF2940

SCI/Mathematics

Mathematics

Second cycle