| Semester 1, 2023 Online | |
| Units : | 1 |
| School or Department : | School of Mathematics, Physics & Computing |
| Grading basis : | Graded |
| Course fee schedule : | /current-students/administration/fees/fee-schedules |
Staffing
Course Coordinator:
Requisites
Pre-requisite: (STA2300 or STA1003 or equivalent) and (MAT1102 or ENM1600)
Overview
Statistics plays a vital role in social and scientific investigations. This course introduces students to the theory of probability and probability distributions, with clear indication of the relevance and importance of the theory in solving practical problems in the real world. The development of these concepts, and the understanding of the properties of commonly used distributions and underlying theory, form a solid foundation for the subsequent course on statistical inference.
This course introduces students to the concepts and elements of probability and distribution theory. The topics include probability, random variables and their distributions, expectation, moment generating functions, standard discrete and continuous distributions, bivariate distributions, transformation techniques and sampling distributions related to the normal distribution. This course also includes practical applications of these distributions and introduces statistical computations using R.
Course learning outcomes
On successful completion of this course students will be able to:
- Define probability concepts and identify properties of commonly used distributions.
- Derive probability distributions and functions of random variables.
- Evaluate the appropriateness of probability models to a variety of contexts.
- Apply a statistical package to evaluate the probability of suitably defined events and related applications.
- Communicate probability and probability distributional results using appropriate terminology for expert and non-expert audiences.
Topics
| Description | Weighting(%) | |
|---|---|---|
| 1. | Probability - sample spaces and events, probability axioms, conditional probability, Bayes' Theorem, permutations and combinations. | 15.00 |
| 2. | Random Variables - discrete, continuous and mixed, mass functions, density functions, distribution functions, bivariate distributions, marginal and conditional mass and density functions | 15.00 |
| 3. | Expectation and Moments - mathematical expectation, algebra of expectations, covariance and correlation, conditional expectation, moments, moment generating functions, order statistics | 15.00 |
| 4. | Standard Discrete Distributions - uniform, binomial, geometric, negative binomial, hypergeometric, Poisson | 15.00 |
| 5. | Standard Continuous Distributions - uniform, gamma, exponential, beta, normal, bivariate normal | 15.00 |
| 6. | Transformations - distribution function, moment generating function and change of variables methods applied to discrete and continuous random variables in one and two dimensions | 15.00 |
| 7. | Introduction to Bayesian statistics | 10.00 |
Text and materials required to be purchased or accessed
Student workload expectations
To do well in this subject, students are expected to commit approximately 10 hours per week including class contact hours, independent study, and all assessment tasks. If you are undertaking additional activities, which may include placements and residential schools, the weekly workload hours may vary.
Assessment details
| Description | Group Assessment |
Weighting (%) |
|---|---|---|
| Problem Solving 1 | No | 15 |
| Problem Solving 2 | No | 25 |
| Problem Solving 3 | No | 20 |
| Report A1 of 2 | No | 20 |
| Report A2 of 2 | No | 20 |