# SF1935 Probability Theory and Statistics with Application to Machine Learning 7.5 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. The course provides a foundational understanding of machine learning, building on probability theory and statistics.

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Headings with content from the Course syllabus SF1935 (Spring 2023–) are denoted with an asterisk ( )

## Content and learning outcomes

### Course contents

Basic concepts such as probability, conditional probability and independent events. Discrete and continuous stochastic variables, especially one-dimensional stochastic variables. Location, spread and dependency measures for stochastic variables and data sets. Common distributions and their model situations, including the normal distribution, the binomial distribution and the Poisson distribution. The Central limit value theorem and the Law of large numbers.

Descriptive statistics. Point estimates and general estimation methods such as the Maximum likelihood method and the Minimum square method. General confidence intervals but special confidence intervals for expected value and variance in normal distribution. Confidence interval for participations and difference in expected values and participations. Hypothesis testing. Chi2 test of distribution, homogeneity test and independence test. Linear regression.

Machine learning paradigms, appoaches and applications. Supervised / unsupervised learning, generalization, model selection, validation and evaluation, probabilistic methods, dimensionality reduction and representations.

### 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 statistical theory
• carry out a project work in a group with oral or written presentation and apply machine learning methods for data analysis problems

### Course disposition

No information inserted

## Literature and preparations

### Specific prerequisites

Completed course SF1625 Calculus in One Variable

### Recommended prerequisites

No information inserted

### Equipment

No information inserted

### Literature

No information inserted

## 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 work, 1.5 credits, grading scale: P, F
• TEN1 - Written exam, 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.

### 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 SF1935

### Main field of study

This course does not belong to any Main field of study.

First cycle