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# STA2301 Distribution Theory

 Semester 1, 2022 Online Units : 1 Faculty or Section : Faculty of Health, Engineering and Sciences School or Department : School of Mathematics, Physics & Computing Student contribution band : Band 1 Grading basis : Graded Version produced : 18 May 2022

## Staffing

Examiner: Enamul Kabir

## Requisites

Pre-requisite: (STA2300 or STA1003 or equivalent) and (MAT1102 or ENM1600)

## Overview

Statistics plays a vital role in social and scientific investigations. This course introduces students to the theory of probability and probability distributions, with clear indication of the relevance and importance of the theory in solving practical problems in the real world. The development of these concepts, and the understanding of the properties of commonly used distributions and underlying theory, form a solid foundation for the subsequent course on statistical inference.

This course introduces students to the concepts and elements of probability and distribution theory. The topics include probability, random variables and their distributions, expectation, moment generating functions, standard discrete and continuous distributions, bivariate distributions, transformation techniques and sampling distributions related to the normal distribution. This course also includes practical applications of these distributions and introduces statistical computations using R.

## Course learning outcomes

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

1. Define probability concepts and identify properties of commonly used distributions.
2. Derive probability distributions and functions of random variables.
3. Evaluate the appropriateness of particular probability models to a variety of contexts.
4. Apply a statistical package to evaluate the probability of suitably defined events and related applications.
5. Communicate probability and probability distributional results using appropriate terminology for expert and non-expert audiences.

## Topics

Description Weighting(%)
1. Probability - sample spaces and events, probability axioms, conditional probability, Bayes' Theorem, permutations and combinations. 15.00
2. Random Variables - discrete, continuous and mixed, mass functions, density functions, distribution functions, bivariate distributions, marginal and conditional mass and density functions 15.00
3. Expectation and Moments - mathematical expectation, algebra of expectations, covariance and correlation, conditional expectation, moments, moment generating functions, order statistics 15.00
4. Standard Discrete Distributions - uniform, binomial, geometric, negative binomial, hypergeometric, Poisson 15.00
5. Standard Continuous Distributions - uniform, gamma, exponential, beta, normal, bivariate normal 15.00
6. Transformations - distribution function, moment generating function and change of variables methods applied to discrete and continuous random variables in one and two dimensions 15.00
7. Introduction to Bayesian statistics 10.00

## Text and materials required to be purchased or accessed

Wackerly, DD, Mendenhall, W & Schaeffer, RL 2008, Mathematical statistics with applications, 7th edn, Duxbury, Pacific Grove, CA.
All additional study material will be provided on the course StudyDesk.