Probability and Distribution Theory (PDT)

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.


Coordinator

Semesters 1: Prof Andrew Forbes, Dept of Epidemiology & Preventive Medicine, Monash University

Semesters 2: Prof Rory Wolfe, Dept of Epidemiology & Preventive Medicine, Monash University


COORDINATORS:
Prof Andrew Forbes Monash University, Department of Epidemiology and Preventive Medicine Semester 1
Dr Jessica Kasza Monash University, Department of Epidemiology and Preventive Medicine Semester 2
General outline

Prerequisites

Mathematical Background for Biostatistics

Time commitment

8-12 hours total study time per week

Semester availability

Semester 1 & 2

Assessment

Two written assignments, each worth 35% and submission of selected practical written exercises from 5 modules 30%.

Prescribed Texts

Wackerly DD, Mendenhall W, Scheaffer RL. Mathematical Statistics with Applications, 7th edition, 2007, Wadsworth Publishing (ex Duxbury Press, USA) For details, including ISBN, see the BCA Textbook and Software Guide

Special Computer Requirements

Stata or R statistical software, WolframAlpha

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 are used throughout to demonstrate concepts.

Special Computer Requirements

Course notes, assignment material and interaction facilities available online