# Probability and Distribution Theory (BSTA5023)

## UNIT OF STUDY

This unit will focus on applying the calculus-based techniques learned in Mathematical Background for Biostatistics (MBB) to the study of probability and statistical distributions. These two units, together with the subsequent Principles of Statistical Inference (PSI) unit, will provide the core prerequisite mathematical statistics background required for the study of later units in the Graduate Diploma or Masters degree. Content: This unit begins with the study of probability, random variables, discrete and continuous distributions, and the use of calculus to obtain expressions for parameters of these distributions such as the mean and variance. Joint distributions for multiple random variables are introduced together with the important concepts of independence, correlation and covariance, marginal and conditional distributions. Techniques for determining distributions of transformations of random variables are discussed. The concept of the sampling distribution and standard error of an estimator of a parameter is presented, together with key properties of estimators. Large sample results concerning the properties of estimators are presented with emphasis on the central role of the Normal distribution in these results. General approaches to obtaining estimators of parameters are introduced. Numerical simulation and graphing with Stata is used throughout to demonstrate concepts.

## Further unit of study information

### Classes

8-12 hours total study time per week, distance learning

### Assessment

practical written exercises (30%) and 2x written assignments (35% each)

### Textbooks

Wackerly DO, Mendenhall W, Scheaffer RL. Mathematical Statistics with Applications, 7th edition, 2007, Brooks/Cole, Cengage Learning, USA. ISBN 978-0-495-11081-1 Notes supplied

No

BSTA5001

## Study this unit outside a degree

### Non-award/non-degree study

If you wish to undertake one or more units of study (subjects) for your own interest but not towards a degree, you may enrol in single units as a non-award student.

### Cross-institutional study

If you are from another Australian tertiary institution you may be permitted to underake cross-institutional study in one or more units of study at the University of Sydney.