Foundations of Probability Theory

Description

This unit introduces the key concepts in probability and distribution theory, including probability laws, random variables, expectation and variance, conditional probabilities, functions of random variables and multivariate probability distributions. Emphasis is placed on theoretical understanding combined with problem solving using algebra and calculus-based methods.

Availability

Distance Education - Callaghan

  • Semester 2 - 2017

Learning Outcomes

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

1. Understand of the principles of probability theory;

2. Recognise common probability distributions for discrete and continuous variables;

3. Apply methods from algebra and calculus to derive the mean and variance for a range of probability distributions;

4. Calculate probabilities relevant to multivariate distributions, including marginal and conditional probabilities and the covariance of two random variables;

5. Derive probability distributions relevant to functions of random variables;

6. Understand the concept of an estimator, common methods for evaluating an estimator¿s performance and properties of desirable estimators;

7. Understand the central limit theorem and large-sample approximations for common statistics;

8. Perform simple Monte Carlo simulations to gain deeper insight into statistical principles.

Content

This subject presents an overview of the probability and distribution theory required to understand statistical inference. Students will study the basic theory and laws of probability. They will then be introduced to random variables and gain an understanding of their properties through studying univariate probability distributions. Multivariate distributions will then be introduced, together with conditional probabilities, methods for evaluating the joint behaviour of multiple random variables, and functions of random variables. Principles of statistical estimation will be discussed and key properties of statistical estimators defined. Students will also gain basic experience in the use of simulation methods to understand statistical concepts.

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