Lecture Notes
Please use the textbook as your primary study tool. The lecture notes is a summarised version and you could be tested on things that is not captured in them.
Week 1
- Lecture 1 - Module Introduction and The Mathematics of Probability - Video recording
- Lecture 2 - Probability Axioms and Conditional Probability - Video recording
- Lecture 3 - Total Probability, Bayes' Theorem and Independence - 2026 video recording (poor audio) - 2024 video recording
Week 2
- Lecture 4 - Sequential Experiments - Video recording
- Lecture 5 - Discrete Random Variables and Probability Mass Functions - Video recording
- Lecture 6 - Cumulative Distribution Functions (CDF); Averages and Expected Values; Functions of a Random Variable - Video recording
Week 3
- (Mini-Lecture on Python and probability theory - (slides HERE) - Google Colab Tutorial)
- Lecture 7 - Expected Value of a Derived Random Variables and Variance and Standard Deviation - Video recording
- Lecture 8 - Families of Discrete Random Variables (Part 1) - Video recording
- Lecture 9 - Families of Discrete Random Variables (Part 2) - Video recording
Week 4
- No Monday lecture - Women's Day timetable adjustment
- Lecture 10 - Continuous Sample Space; The Cumulative Distribution Function; Probability Density Function; Expected Values - Video recording
- Lecture 11 - Families of Continuous Random Variables - Video recording
Week 5
- Lecture 12 - Gaussian Random Variables - Video recording
- Lecture 13 - Delta Functions, Mixed Random Variables - Video recording
- Lecture 14 - Joint Cumulative Distribution Function & Joint Probability Mass Function & Marginal PMF - Video recording
Week 6
- Lecture 15 - Joint Probability Density Function & Marginal PDF - Video recording
- Lecture 16 - Independent Random Variables & Expected Value of a Function of Two Random Variables & Covariance, Correlation and Independence - Video recording
- Lecture 17 - Bivariate Gaussian Random Variables & Multivariate Probability Models - Video recording - Code
Week 7: Test Week
Assessment Dates:
- A1: Tuesday, September 1, 2026 at 11:00
- A1 (2026) - Formula Sheet
Venue Allocation
Students must report to the following venue according to surname:
- E2005: Adams to Meintjes
- E2002: Mervis to Zhu
Students with approved extra writing time must report to E2002, regardless of surname.
Please ensure that you report directly to the correct venue.
The following content is from 2025 and has not been updated to 2026 yet. Things are subject to
change.
Week 8
- Lecture 18 - Probability Models of Derived Random Variables
- Lecture 19 - Conditional Probability Models: Conditioning by an Event
- Lecture 20 - Conditional Probability Models: Conditioning by a Random Variable
Week 9
- Lecture 21 - Random Vectors: Notation, Independence, Functions of Random Vectors
- Lecture 22 - Random Vectors: Expected Value Vector and Correlation Matrix, Gaussian Random Vectors
- No lecture - Heritage Day
Week 10
Lectures 23–25 will not be presented in person in 2026. I will be away attending a
conference. Please watch the corresponding 2024 video recordings linked below.
The tutorial and tutorial test will proceed as normal.
- Lecture 23 - Moment Generating Functions & Sums of Random Variables - 2024 video recording
- Lecture 24 - Central Limit Theorem & The Sample Mean & Deviation of RV from the Expected Value - 2024 video recording
- Lecture 25 - Laws of Large Number & Point Estimates of Model Parameters - 2024 video recording
Week 11
- Lecture 26 - Hypothesis Testing
- Lecture 27 - Estimation of a Random Variable
- Lecture 28 - Stochastic Processes
Week 12
- Lecture 29 - The Poisson Process
- Lecture 30 - The Brownian Motion Process & Expected Value and Correlation & Moments
- Lecture 31 - Stationary Processes & Wide Sense Stationary Stochastic Processes
Week 13
- Lecture 32 - Cross-correlation & Gaussian Processes
- Lecture 33 - Power Density Spectrum
- Revision Lecture
A2/A3
- A2: Wednesday, November 18, 2026 at 09:00
- A3: Thursday, December 3, 2026 at 09:00
- A2/A3 2025 Formula Sheet
Archive
Class notes from 2025
Lectures 1 and 2 are dated 2024.
- Lecture 1 class notes (2024)
- Lecture 2 class notes (2024)
- Lecture 3 class notes
- Lecture 4 class notes
- Lecture 5 class notes
- Lecture 6 class notes
- Lecture 7 class notes
- Lecture 8 class notes
- Lecture 9 class notes
- Lecture 10 class notes
- Lecture 11 class notes
- Lecture 12 class notes
- Lecture 13 class notes
- Lecture 14 class notes
- Lecture 15 class notes
- Lecture 16 class notes
- Lecture 17 class notes
- Lecture 18 class notes
- Lecture 19 class notes
- Lecture 20 class notes
- Lecture 21 class notes
- Lecture 22 class notes
- Lecture 23 class notes
- Lecture 24 class notes
- Lecture 25 class notes
- Lecture 26 class notes
- Lecture 27 class notes
- Lecture 28 class notes
- Lecture 29 class notes
- Lecture 30 class notes
- Lecture 31 class notes
- Lecture 32 class notes
- Lecture 33 class notes
Video lectures from 2024
- Lecture 1 recording
- Lecture 2 recording
- Lecture 3 recording
- Lecture 4 recording
- Lecture 5 recording
- Lecture 6 recording
- Lecture 7 recording
- Lecture 8 recording
- Lecture 9 recording
- Lecture 10 recording
- Lecture 11 recording
- Lecture 12 recording
- Lecture 13 recording
- Lecture 14 recording
- Lecture 15 recording
- Lecture 16 recording
- Lecture 17 recording
- Lecture 18 recording
- Lecture 19 recording
- Lecture 20 recording
- Lecture 21 recording
- Lecture 22 recording
- Lecture 23 recording
- Lecture 24 recording
- Lecture 25 recording
- Lecture 26 recording
- Lecture 27 recording
- Lecture 28 recording
- Lecture 29 recording
- Lecture 30 recording
- Lecture 31 recording
- Lecture 32 recording
- Lecture 33 recording
Tutorials
Wednesdays 14:00-17:00 in K303 or M3002 (usually K303)
- Tutorial 1 - Memo - Tutorial Test 1 memo
- Tutorial 2 - Memo - Tutorial Test 2 memo
- Tutorial 3 - Memo - Tutorial Test 3 memo
- Week 4 self-study: 2025 Tutorial 4 - 2025 Memo - 2025 Tutorial Test 4 memo (Self study)
- Tutorial 5 - Memo - Tutorial Test 5 memo
- Tutorial 6 - Memo - Tutorial Test 6 memo
Resources
- Bilingual list of terms / Tweetalige lys van terme
- Yates & Goodman Chapters 1 & 2
- 2021 Afrikaans Summaries
- Python Introduction Tutorial - Helpful for Practical sessions
- Formula sheets for 2024: A1, A2/A3
Additional Helpful Resources
These resources provide alternative explanations, worked examples, and visual intuition. Please continue to use the prescribed textbook and lecture notes as your primary study material. If you find another useful resource, please send it to rptheart@sun.ac.za.
External links checked July 2026.
Recommended starting points
- Introduction to Probability, Statistics, and Random Processes — A free, peer-reviewed textbook aimed at engineering students, with examples, short videos, and calculators.
- MIT OpenCourseWare: Probabilistic Systems Analysis — A complete self-study course with lectures, tutorials, problems, and solutions.
- Harvard Statistics 110 — A rigorous probability course with a free textbook, lecture videos, and practice problems.
- Seeing Theory — Interactive visualisations of probability, distributions, and inference. The creators now maintain it as an archived reference.
- 3Blue1Brown: Probability — Visual explanations of Bayes' theorem, distributions, the central limit theorem, and related ideas.
Quick topic links
- Sets, counting, conditional probability, and Bayes' theorem
- Cumulative distribution functions
- Expected values
- Functions of random variables
- Variance
- Common discrete distributions
- NIST gallery of common probability distributions
- Solved joint probability density problems