# STAT20100 Inferential Statistics

Probability theory, large sample theory, statistical inference. Purpose: create a mathematical framework to study random phenomena, and to make decisions in a state of uncertainty.

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Curricular information is subject to change

Learning Outcomes:

A good understanding of multivariate probability distributions, including conditional and marginal distributions. An ability to calculate and understand covariance and correlation coefficients. A knowledge and appreciation of the central limit theorem. A good understanding of the theory of estimation, including various methods for estimating parameters either with point estimates or confidence interval estimates. An ability to formulate and test statistical hypotheses and statements. An understanding of the methodology of many commonly used statistical tests. A good understanding of the principles of statistical decision theory and of optimality of estimators.

Indicative Module Content:

Probability theory: Continuous bivariate and multivariate distributions. Covariance and correlation. Chebyshev inequality. Law of Large Numbers. Central Limit Theorem and applications.

Statistics: Theory of Estimation. Method of moments, and maximum likelihood. Point and interval estimation. Properties and optimality of estimators. Hypothesis Testing. Simple and Composite Hypotheses. Neyman-Pearson Lemma and applications. Likelihood ratio tests. Introduction to statistical decision theory.

Student Effort Hours:
Student Effort Type Hours
Lectures

24

Tutorial

20

Specified Learning Activities

20

Autonomous Student Learning

50

Total

114

Approaches to Teaching and Learning:
Weekly lectures, weekly tutorials, homework assignments.
Requirements, Exclusions and Recommendations
Learning Requirements:

Calculus: familiarity with differentiation and integration. A knowledge of probability theory and random variables: probability theory, combinatorics and classic discrete and continuous random variables. Means and variances. Standard probability distributions: binomial, geometric, Poisson, normal, exponential, gamma, beta, chi-square.

Learning Recommendations:

A knowledge of probability to the level of the Probability Theory course (STAT20110).

Module Requisites and Incompatibles
Incompatibles:
STAT30280 - Inference for Data Analyti(OL)

Assessment Strategy
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade
Assignment(Including Essay): Take-home assignments n/a Other No

20

Exam (In-person): 2 hours end of trimester exam n/a Other No

80

Carry forward of passed components
No

Resit In Terminal Exam
Autumn Yes - 2 Hour