# Foundations of Probability (Autumn 2023)

#### Official course description:

##### Course info

##### Programme

##### Staff

##### Course semester

##### 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.

##### Learning activities

The taught part of the course comprises 14 weeks of lectures and exercises.

Through exercises the students practice solving basic problems in probability theory and presenting orally the solutions. Students are expected to prepare before the exercise sessions by (at least) attempting to solve the problems on the weekly problem sheet.

##### Mandatory activities

There are six mandatory assignments -- one roughly every two weeks throughout the semester. All six assignments must be approved to qualify for the exam. Opportunities for re-submission of non-approved assignments will be given.

The mandatory assignments form an integral part of the learning activities and ensures that all students get extensive feedback on written work.

The student will receive the grade NA (not approved) at the ordinary exam, if the mandatory activities are not approved and the student will use an exam attempt.

##### Course literature

*Introduction to
Probability* (second edition,
by Joseph K. Blitzstein & Jessica Hwang)

##### Student Activity Budget

Estimated distribution of learning activities for the typical student- Preparation for lectures and exercises: 40%
- Lectures: 14%
- Exercises: 14%
- Assignments: 14%
- Exam with preparation: 18%

##### Ordinary exam

**Exam type:**

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

**Exam variation:**

A33: Written exam on premises on paper with restrictions

**Exam duration:**

4 hours

**Aids allowed for the exam:**

Written and printed books and notes

Pen

Calculator

E-books and/or other electronic devices

- Access to e-books, also on laptops and iPads is permitted, access to course notes as well as personal notes on laptops, iPads and the like is permitted.

##### reexam

**Exam type:**

X: Experimental form, External (7-point scale)

**Exam variation:**

X: Experimental form

**Exam submission description:**

The re-exam format will be the same as the ordinary exam, unless 10 or fewer students are registered for the re-exam, in which case the format will be an individual oral exam: B11 exam form, external (7-trinskala). Oral exam with preparation inhouse. 20 minutes in-house preparation time and 20 minutes oral examination.

##### Time and date

Ordinary Exam - on premises Mon, 18 Dec 2023, 09:00 - 13:00Reexam - on premises Fri, 8 Mar 2024, 11:00 - 20:00