Overview
This course develops the mathematical foundations of probability for study in statistics, data science, mathematics, and related quantitative disciplines. Topics include sample spaces and events, set notation, counting principles, permutations and combinations, probability axioms, conditional probability, independence, Bayes’ theorem, and discrete and continuous random variables.
Students examine probability mass, density, and cumulative distribution functions; expected value, variance, standard deviation, covariance, correlation, and transformations of random variables; and common Bernoulli, binomial, geometric, hypergeometric, Poisson, uniform, exponential, and normal models. Emphasis is placed on formulating probability models, interpreting assumptions, distinguishing conditional probability from independence, applying Bayes’ theorem, identifying suitable distributions, and using simulation to investigate probabilistic behaviour.
Learning Outcomes
- Formulate probability models using precise sample-space, event, and set notation.
- Apply counting principles, permutations, combinations, and probability axioms to calculate event probabilities.
- Distinguish conditional probability from independence and apply Bayes’ theorem to inverse probability problems.
- Identify and evaluate discrete and continuous random-variable models using probability mass, density, and cumulative distribution functions.
- Compute and interpret expected values, variances, standard deviations, covariances, and correlations.
- Select and justify suitable common probability distributions for applied modelling contexts.
- Derive and apply transformations of random variables in discrete and continuous settings.
- Use simulation, graphical methods, and symbolic reasoning to investigate and communicate probabilistic behaviour.
Timetable
| Type | Length | Frequency | Period |
|---|---|---|---|
| Lecture | 2 hours | Weekly | All semester |
| Tutorial | 1 hour | Weekly | All semester |
| Lab | 2 hours | Fortnightly | All semester |
Assessment Schedule
| Type | Description | Weighting |
|---|---|---|
| Assignment | Probability modelling assignment | 15.00% |
| Quiz | Quizzes (4 × 5%) | 20.00% |
| Deliverable | Simulation and data analysis report | 15.00% |
| Test | Mid-semester test | 20.00% |
| Exam | Final examination | 30.00% |
Prerequisites
- Requirement 14 NCEA Level 2 Mathematics credits, externally assessed
Teaching Staff & Programs
This course is delivered jointly by faculty from the participating programs listed below. In line with the Douchewater Way, the University of Sexology tailors core instruction directly to each cohort's specific discipline — adapting curriculum to program needs rather than forcing students into a one-size-fits-all model. Learn more about our approach at The Douchewater Way.