# SF1901 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.

Course offerings are missing for current or upcoming semesters.
Headings with content from the Course syllabus SF1901 (Autumn 2007–) are denoted with an asterisk ( )

## Content and learning outcomes

### Course contents

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.

### 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

• 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 differential and integral calculus.

### Recommended prerequisites

No information inserted

### Equipment

No information inserted

### Literature

Blom et al. Sannolikhetslära 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.

### Other requirements for final grade

Written examination.

### 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 SF1901

### Main field of study

Mathematics, Technology

First cycle