STA2301 Distribution Theory

STA	2301	74231	1, 2008	ONC	Distribution Theory	1.00	Toowoomba
Subject	Cat-nbr	Class	Term	Mode	Description	Units	Campus

Academic group:	FOSCI
Academic org:	FOS003
Student contribution band:	2
ASCED code:	010103

Staffing
Requisites
Rationale
Synopsis
Objectives
Topics
Texts
Reference materials
Student workload
Assessment details
Important assessment information
Assessment notes
Production date
PDF version

STAFFING

Moderator: Ashley Plank

REQUISITES

Pre-requisite: (STA2300 and MAT1102) or Students must be enrolled in one of the following Programs: MSBN or MSMS

RATIONALE

To develop the methodology of statistics in subsequent courses, an understanding of the concepts and theory of probability and probability distributions is required and is provided by this course.

SYNOPSIS

This course introduces students to the 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.

OBJECTIVES

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

compute probabilities for various situations (Assignment 1, Exam);
derive some standard discrete and continuous probability distributions and apply them appropriately (Assignment 2 & 3, Exam);
derive the marginal and conditional distribution of random variables (Assignment 2 & 3, Exam);
compute the conditional mean and variance from given bivariate distribution (Assignment 3, Exam);
understand the concept and applications of the moment generating function (Assignment 2 & 3, Exam);
obtain the distribution of transformed variables defined on one and two dimensional space (Assignment 3, Exam);
derive the sampling distributions of some statistics (Assignment 3, Exam);
use a computer package to solve relevant statistical problems when appropriate (Assignments 1, 2 & 3, Exam).

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	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.	Sampling Distributions (t, F and chi-squared), Central Limit Theorem.	10.00

TEXT and MATERIALS required to be PURCHASED or accessed

ALL textbooks and materials are available for purchase from USQ BOOKSHOP (unless otherwise stated). Orders may be placed via secure internet, free fax 1800642453, phone 07 46312742 (within Australia), or mail. Overseas students should fax +61 7 46311743, or phone +61 7 46312742. For costs, further details, and internet ordering, use the 'Textbook Search' facility at http://bookshop.usq.edu.au click 'Semester', then enter your 'Course Code' (no spaces).

Introductory Book 2008, STA2301 Distribution Theory, USQ Distance and e-Learning Centre, Toowoomba.

Study Book 2008, STA2301 Distribution Theory, USQ Distance and e-Learning Centre, Toowoomba.

Wackerly, D.D, Mendenhall, W. & Schaeffer, R.L 2002, Mathematical Statistics with Applications, 6th edn, Duxbury, Pacific Grove, CA.

REFERENCE MATERIALS

Reference materials are materials that, if accessed by students, may improve their knowledge and understanding of the material in the course and enrich their learning experience.

MATLAB, current version, Student Edition, CD and Users Guide.

Berry, D.A. & Lindgren, B.W 1996, Statistics: Theory and Methods, 2nd edn, Duxbury Press, Belmont.

Freund, J.E. & Walpole, R.E 1992, Mathematical Statistics, 5th edn, Prentice-Hall, Englewood Cliffs.

Hogg, R.V. & Craig, A.T 1995, Introduction to Mathematical Statistics, 5th edn, Prentice Hall, Englewood Cliffs.

Larsen, R.J. & Marx, M.L 2006, An Introduction to Mathematical Statistics and its Applications, 4th edn, Prentice-Hall, Englewood Cliffs.

STUDENT WORKLOAD REQUIREMENTS

ACTIVITY	HOURS
Assessment	20.00
Examinations	2.00
Lectures	26.00
Private Study	98.00
Tutorials	26.00

ASSESSMENT DETAILS

Description	Marks out of	Wtg(%)	Due date	Notes
ASSIGNMENT 1	100.00	10.00	28 Mar 2008
ASSIGNMENT 2	100.00	15.00	02 May 2008
ASSIGNMENT 3	100.00	15.00	30 May 2008
EXAM 2HR RESTRICTED	100.00	60.00	END S1	(see note 1)

NOTES

1.: Examination dates will be available during the Semester. Please refer to Examination timetable when published.

IMPORTANT ASSESSMENT INFORMATION

Attendance requirements:
It is the students' responsibility to attend and participate appropriately in all activities (such as lectures, tutorials, laboratories and practical work) scheduled for them, and to study all material provided to them or required to be accessed by them to maximise their chance of meeting the objectives of the course and to be informed of course-related activities and administration.
Requirements for students to complete each assessment item satisfactorily:
To complete each of the assessment items satisfactorily, students must obtain at least 50% of the marks available for each assessment item.
Penalties for late submission of required work:
If students submit assignments after the due date without (prior) approval of the examiner then a penalty of 5% of the total marks gained by the student for the assignment may apply for each working day late up to ten working days at which time a mark of zero may be recorded. No assignments will be accepted after model answers have been posted.
Requirements for student to be awarded a passing grade in the course:
To be assured of receiving a passing grade a student must achieve at least 50% of the total weighted marks available for the course.
Method used to combine assessment results to attain final grade:
The final grades for students will be assigned on the basis of the weighted aggregate of the marks obtained for each of the summative assessment items in the course.
Examination information:
In a Restricted Examination, candidates are allowed access to specific materials during the examination. The only materials that candidates may use in the restricted examination for this course are: writing materials (non-electronic and free from material which could give the student an unfair advantage in the examination); calculators which cannot hold textual information (students must indicate on their examination paper the make and model of any calculator(s) they use during the examination) and Formula sheets as provided by the Examiner with the examination paper. Students whose first language is not English, may, with the Examiner's approval, take an appropriate non- electronic translation dictionary into the examination. Students who wish to use a translation dictionary MUST request and receive written approval from the Examiner at least one week before the examination date. Translation dictionaries will be subject to perusal and may be removed from the candidate's possession until appropriate disciplinary action is completed if found to contain material that could give the candidate an unfair advantage.
Examination period when Deferred/Supplementary examinations will be held:
Any Deferred or Supplementary examinations for this course will be held during the examination period at the end of the semester of the next offering of this course.
University Regulations:
Students should read USQ Regulations 5.1 Definitions, 5.6. Assessment, and 5.10 Academic Misconduct for further information and to avoid actions which might contravene University Regulations. These regulations can be found at the URL http://www.usq.edu.au/corporateservices/calendar/part5.htm or in the current USQ Handbook.

ASSESSMENT NOTES

The due date for an assignment is the date by which a student must despatch the assignment to the USQ. The onus is on the student to provide proof of the despatch date, if requested by the Examiner. Students must retain a copy of each item submitted for assessment. This must be despatched to USQ within 24 hours of receiving a request from the examiner to do so. The examiner may grant an extension of the due date of an assignment in extenuating circumstances.

This version produced 6 Aug 2008.