University of Wollongong - STAT201: Random Variables and Estimation

This subject, Random Variables and Estimation (STAT201) - is the second statistics subject following STAT101. It provides the theoretical foundation (introductory probability theory) for more advanced statistics subjects which rely on this theory. It builds on STAT101 and introduces new discrete random variables (Poisson distribution, Hypergeometric, Uniform) and new continuous random variables (Exponential and Gamma distributions, Uniform, Beta and Cauchy), and teaches concepts such as expected values; transformations; moment generating functions; mutlivariate distributions; the Law of large numbers; and the Central Limit Theorem. STAT201 also introduces the major estimation and hypothesis testing concepts and many common analysis techniques. Topics include inference techniques, which include sampling distributions (such as the chi-squared, t and F distributions), methods and criteria of estimation. and hypothesis testing and investigates the relationship between Size, Power and sample size. Students will learn a popular freely available statistical software package that has become increasingly important in recent years in academia, and in the job market.

✔ On successful completion of this subject, you will be able to: 

• explain and apply the basic concepts of probability;
• build probability models for random variables;
• derive properties of probability models for random variables;
• derive the moments of distributions directly and by using moment generating functions;
• derive and apply transformations of random variables;
• simulate various random variables and explain the use of simulation;
• interpret and model practical problems;
• explain the basic concepts of sampling theory, point and interval estimation, and hypothesis testing;
• apply and interpret appropriate procedures from a statistical package such as R; and, 
• communicate results and conclusions from a statistical analysis in a clear manner.