# Probability and Distribution Theory

Course code BIOS6170
Available in 2016
Units 10
Level 6000

## Description

This unit involves the study of basic probability and calculus-based methods underpinning probability distributions, and parameter estimation. It begins with the concepts of probability, random variables, discrete and continuous distributions, and then discusses the use of calculus to obtain expressions for key parameters of these distributions, such as the mean and variance, and to investigate transformations of these distributions. Methods of estimation of these parameters based on a random sample from a probability distribution will then be presented. The central role of the normal distribution will be emphasised, together with transformations to normality and large sample properties of estimators. Numerical simulation will be used as a tool to demonstrate key concepts.

This course is offered in conjunction with the Biostatistics Collaboration of Australia (BCA)

### Availability

#### Distance Education - Callaghan

• Semester 1 - 2016
• Semester 2 - 2016
• Semester 1 - 2017
• Semester 2 - 2017

### Learning Outcomes

On successful completion of the course students will be able to:

1. Demonstrate an understanding of the meaning and laws of probability

2. Apply calculus-based tools to derive key features of a probability distribution, such as mean and variance

3. Understand the theoretical basis for estimation via likelihood based methods

4. Apply calculus based tools to derive estimators from likelihood functions

5. Understand properties of parameter estimators and the usefulness of large sample approximations in statistics

6. Appreciate the role of simulation in demonstrating and explaining statistical concepts

### Content

The teaching mode is off-campus. Written material together with selected textbook readings and biostatistical applications will introduce basic concepts. Detailed study of the theoretical derivation of basic probability and distribution theoretic results together with numerical simulation will provide a deeper understanding of important general principles (objectives 1,2,6). Statistical estimation will be introduced using first principles and properties demonstrated by theory and numerical simulation (objectives 3,4,5,6). A key component of students' learning will be to attempt many of the suggested exercises (objectives 2,3,4,5). Structured practical exercises for assessment will give students the ability to provide theoretical justification for standard estimation procedures and prepare students to be able to apply general estimation principles in more complex settings (objective 3,4,5). Structured on-line exercises will provide students with an opportunity to demonstrate their understanding of key concepts, to receive feedback, and obtained responses to queries from unit coordinators and other students (objectives 1-6).

### Requisite

Must be enrolled in Graduate Diploma of Medical Biostatistics or Master of Medical Statistics to enrol in this course. Pre-requisites: must have successfully completed BIOS6040.

### Assessment Items

Written Assignment: Essays / Written Assignments

Written Assignment: Practical Written Exercise

### Contact Hours

#### Distance Education - Callaghan

##### Online Activity

Online 2 hour(s) per Week for Full Term

##### Self-Directed Learning

Self-Directed 8 hour(s) per Week for Full Term