Probability and Statistical Inference (MAS222) - at Murdoch University

This unit examines relevant topics in probability and statistics theory, including distribution theory, mathematical expectation and variance, and likelihood inference. It derives common probability distributions and illustrates their uses, provides insight into the forms of expected values and variances for various distributions, and introduces likelihood inference, which provides a unified framework that underpins much of statistical inference.

✔ Learning outcomes:

• Carry out a variety of statistical analyses. In particular, students should be able to: a. compute probabilities, applying rules of addition and multiplication; b. demonstrate an understanding of probability functions and joint probability functions for random variables; c. explain ideas of conditional probability and independence; d. calculate expected values; e. obtain maximum likelihood estimators; f. carry out likelihood ratio tests; and g. demonstrate an understanding of the philosophy of hypothesis testing and statistical estimation.
• Explain conceptually the various statistical methods covered in the unit and the correct application of these methods, and develop a familiarity with computational tools and methods in the context of probability and inference.

✔ Unit content:

Probability theory • Multiplication rule, combinatorics, conditional probability • Random variables, mathematical expectation • Discrete probability distributions • Cumulative distribution function, continuous probability distributions • Joint probability distributions, covariance • The Central Limit Theorem • Likelihood Inference • Properties of estimators • Confidence intervals, hypothesis tests • Wald tests • Likelihood ratio tests