# Probability and Stochastic Modelling 1

Queensland University of Technology

## Course Description

• ### Course Name

Probability and Stochastic Modelling 1

• ### Host University

Queensland University of Technology

• ### Location

Brisbane, Australia

• ### Area of Study

Mathematics, Statistics

• ### Language Level

Taught In English

• ### Course Level Recommendations

Lower

ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.

### Hours & Credits

• Credit Points

12
• Recommended U.S. Semester Credits
3 - 4
• Recommended U.S. Quarter Units
4 - 6
• ### Overview

This unit provides you with an introduction to probability and shows you how to apply its concepts to solve practical problems. The unit will lay the foundations for further studies in statistics, operations research and other areas of mathematics and help you to develop your problem-solving and modelling skills. The topics covered include: basic probability rules, conditional probability and independence, discrete and continuous random variables, bivariate distributions, central limit theorem, goodness-of-fit tests, introduction to Markov chains.

Learning Outcomes
On successful completion of this unit, you should be able to:

1. Apply appropriately the basic concepts of introductory stochastic and statistical modelling.
2. Draw on your knowledge of probability, random variables and distributions to identify and solve problems.
3. Competently and critically build and use stochastic and statistical models for real world problems.
4. Work in a group to solve problems and express a coherent argument.

Content
The topics in this unit develop the fundamental concepts, understanding, knowledge and skills in probability and distributions that are the foundations for models and applications across all of probability and statistics and their applications across disciplines. As a consequence, this unit develops problem-solving skills relevant to all quantitative areas involving chance and data.

The unit does not assume any prior knowledge of probability and distributions (though such knowledge is likely to be of advantage) as this knowledge is developed in the first part of the unit. However, the unit takes for granted the full range of algebraic skills taught up to high school year 10 and builds on a general mathematical understanding and some of the skills (such as integration) that are typically acquired in Senior Mathematics B (or equivalent).

The mathematical content of the unit includes, but is not limited to, all or almost all of the following topics:
- Foundations of probabilistic modelling
Probability rules and language; Kolmogorov axioms; independence and conditional probability; law of total probability and Bayes' rule; discrete and continuous random variables and distributions (such as Bernouilli, binomial, geometric, Poisson, uniform and exponential distributions); expected value and variance; evaluation of model assumptions using goodness of fit tests; introduction to discrete bivariate distributions.

- Introduction to stochastic processes
Simple Markov chains; Poisson processes.

The emphasis throughout is on applications in both familiar and new contexts, and on skills for describing and setting up problems, and identifying methods and tools to solve them. This implies that the focus of this course is not on developing calculation skills, but most of all on developing a conceptual understanding of stochastic and statistical thinking that allows for approaching practical problems by building stochastic and statistical models in a competent, creative and critical way.

Simple strategies for working in groups to solve relevant problems will also be explored to prepare you for group assessment work. The standards for presentation and communication of mathematical and statistical information will be discussed and demonstrated by example.

### Course Disclaimer

Courses and course hours of instruction are subject to change.

Eligibility for courses may be subject to a placement exam and/or pre-requisites.

Some courses may require additional fees.

Credits earned vary according to the policies of the students' home institutions. According to ISA policy and possible visa requirements, students must maintain full-time enrollment status, as determined by their home institutions, for the duration of the program.