# SF2941 Probability Theory and Linear Models 7.5 credits

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.

Course offering missing for current semester as well as for previous and coming semesters
Headings with content from the Course syllabus SF2941 (Autumn 2007–) are denoted with an asterisk ( )

## Content and learning outcomes

### Course contents

The basic concepts of probability theory. Characteristic functions and probability generating functions. Convergence of probability distributions, the Central Limit Theorem. Convergence of random variables. The Law of Large Numbers. Multivariate Normal distributions. Conditional distributions. Linear models and multivariate regression analysis.

### Intended learning outcomes

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

• define and apply basic concepts and methods of probability theory
• use common probability distributions and analyse their properties (exponential distribution, multivariate normal distribution, etc.)
• compute conditional probability distributions and conditional expectations
• solve problems and compute limits of distributions by use of transforms (characteristic functions, probability generating functions,)
• formulate an adequate linear model on the basis of a given problem, such as testing a hypothesis,
• judiciously judge the validity of the specification of a linear model
• estimate the parameters of a linear model, interpret the results, and use the model for prediction and hypothesis testing.

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

### Course disposition

No information inserted

## Literature and preparations

### Specific prerequisites

Basic knowledge in Mathematical Statistics, Fourier Analysis and Linear Algebra.

### Recommended prerequisites

No information inserted

### Equipment

No information inserted

### Literature

Will be determined later.

## 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

• PRO1 - Project, 1,5 hp, betygsskala: P, F
• TEN1 - Examination, 6,0 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.

### Other requirements for final grade

A written examination (TEN1; 6 university credits),
a project task (PRO1; 1,5 university credits)

### Opportunity to complete the requirements via supplementary examination

No information inserted

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

No information inserted

### Examiner

No information inserted

### 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

No information inserted

SCI/Mathematics

### Main field of study

No information inserted

Second cycle