# SF1912 Probability Theory and Statistics 6.0 credits

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.

### Choose semester and course offering

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

Headings with content from the Course syllabus SF1912 (Autumn 2019–) are denoted with an asterisk ( )

## Content and learning outcomes

### Course contents

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.

### Intended learning outcomes

To pass the course, the student should be able to

• solve problems that require knowledge about standard concepts and methods in probability theory
• solve problems that require knowledge about standard concepts and methods in statistics

### Course disposition

No information inserted

## Literature and preparations

### Specific prerequisites

Completed course Calculus in one varible SF1625 or SF1685.

### Recommended prerequisites

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

### Equipment

No information inserted

### Literature

Blom et al., Sannolikhetsteori och statistikteori med tillämpningar, Studentlitteratur

Complemental material from the department.

## 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, 6.0 credits, grading scale: 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.

The examiner decides, in consultation with KTHs Coordinator of students with disabilities (Funka), about any customized examination for students with documented, lasting disability.

### Opportunity to complete the requirements via supplementary examination

No information inserted

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

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

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 SF1912

Technology

First cycle