# Foundations of Probability (Autumn 2024)

#### Official course description, subject to change:

Basic info last published 15/03-24

##### Course info

Language:

English

ECTS points:

7.5

Course code:

BSFOPRO1KU

Participants max:

95

Offered to guest students:

yes

Offered to exchange students:

yes

Offered as a single subject:

yes

Price for EU/EEA citizens (Single Subject):

10625 DKK

##### Programme

Level:

Bachelor

Programme:

BSc in Data Science

##### Staff

##### Course semester

Semester

Efterår 2024

Start

26 August 2024

End

24 January 2025

##### Exam

##### Abstract

The course gives an in-depth introduction to fundamental principles of probability theory.

##### Description

The scope of this course is twofold. First and foremost, the course gives an in-depth introduction to fundamental principles of probability theory. Secondly, via a careful discussion of probabilistic concepts and results the student will be introduced also to mathematical thinking and obtain a fluency in reading, deriving, and communicating mathematical results.

Topics include

- Probabilities.
- Random variables and their distributions
- Joint
and marginal distributions.
- Expectation and variance.
- Transformations of random variables.
- Discrete and continuous distributions
- Statistical independence.
- Conditional probability and Bayes’ theorem.

##### Formal prerequisites

Students are expected to fulfill the admission requirements for the BSc in Data Science.

##### Intended learning outcomes

After the course, the student should be able to:

- Define basic concepts in probability.
- Identify relevant random variables to describe an experiment and relate to standard families of distributions.
- Compute probabilities and conditional probabilities from basic definitions and principles.
- Derive the expectation and variance of a random variable.
- Apply classical results from probability theory to reason about the distribution of a transformation of a random variable
- Formulate or derive a mathematical result and argue for its correctness using appropriate mathematical terminology.

##### Ordinary exam

**Exam type:**

A: Written exam on premises, External (7-point scale)

**Exam variation:**

A33: Written exam on premises on paper with restrictions