STA2301 Distribution Theory
Semester 1, 2013 Oncampus Toowoomba  
Units :  1 
Faculty or Section :  Faculty of Sciences 
School or Department :  Maths and Computing 
Version produced :  21 July 2014 
Staffing
Examiner: Shahjahan Khan
Moderator: Christine McDonald
Requisites
Prerequisite: STA2300 and MAT1102
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;
 derive some standard discrete and continuous probability distributions and apply them appropriately;
 derive the marginal and conditional distribution of random variables;
 compute the conditional mean and variance from given bivariate distribution;
 understand the concept and applications of the moment generating function;
 obtain the distribution of transformed variables defined on one and two dimensional space;
 derive the sampling distributions of some statistics;
 use a computer package to solve relevant statistical problems when appropriate.
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 chisquared), Central Limit Theorem.  10.00 
Text and materials required to be purchased or accessed
ALL textbooks and materials available to be purchased can be sourced from USQ's Online Bookshop (unless otherwise stated). (https://bookshop.usq.edu.au/bookweb/subject.cgi?year=2013&sem=01&subject1=STA2301)
Please contact us for alternative purchase options from USQ Bookshop. (https://bookshop.usq.edu.au/contact/)

Wackerly, DD, Mendenhall, W & Schaeffer, RL 2008, Mathematical statistics with applications, 7th edn, Duxbury, Pacific Grove, CA.

Introductory Book 2013, STA2301 Distribution Theory, accessible from the course StudyDesk.

Study Book 2013, STA2301 Distribution Theory, accessible from the course StudyDesk.
Reference materials

Berry, DA & Lindgren, BW 1996, Statistics: Theory and Methods, 2nd edn, Duxbury Press, Belmont.

Freund, JE & Walpole, RE 1992, Mathematical Statistics, 5th edn, PrenticeHall, Englewood Cliffs.

Hogg, RV & Craig, AT 1995, Introduction to Mathematical Statistics, 5th edn, Prentice Hall, Englewood Cliffs.

Larsen, RJ & Marx, ML 2006, An Introduction to Mathematical Statistics and its Applications, 4th edn, PrenticeHall, Englewood Cliffs.

R package – free download from internet.
Student workload requirements
Activity  Hours 

Assessments  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  15  26 Mar 2013  
ASSIGNMENT 2  100  15  29 Apr 2013  
ASSIGNMENT 3  100  10  27 May 2013  
2HR RESTRICTED EXAM  100  60  End S1  (see note 1) 
NOTES
 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 courserelated 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 (nonelectronic 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, take an appropriate unmarked nonelectronic translation dictionary (but not technical dictionary) into the examination. Dictionaries with any handwritten notes will not be permitted. 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 next examination period. 
University Student Policies:
Students should read the USQ policies: Definitions, Assessment and Student Academic Misconduct to avoid actions which might contravene University policies and practices. These policies can be found at http://policy.usq.edu.au.
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.

The referencing system to be used in this course is supported by the Department. Information on this referencing system and advice on how to use it can be found in the course materials.