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STA2301 Distribution Theory

Semester 1, 2012 External Toowoomba
Units : 1
Faculty or Section : Faculty of Sciences
School or Department : Maths and Computing
Version produced : 30 December 2013

Contents on this page

Staffing

Examiner: Shahjahan Khan
Moderator: Rachel King

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:

  1. compute probabilities for various situations;
  2. derive some standard discrete and continuous probability distributions and apply them appropriately;
  3. derive the marginal and conditional distribution of random variables;
  4. compute the conditional mean and variance from given bivariate distribution;
  5. understand the concept and applications of the moment generating function;
  6. obtain the distribution of transformed variables defined on one and two dimensional space;
  7. derive the sampling distributions of some statistics;
  8. 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 chi-squared), 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=2012&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 2012, STA2301 Distribution Theory, included in the course CD.
  • Study Book 2012, STA2301 Distribution Theory, included in the course CD.

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.
  • Berry, DA & Lindgren, BW 1996, Statistics: Theory & Methods, 2nd edn, Duxbury Press, Belmont.
  • Freund, JE & Walpole, RE 1992, Mathematical Statistics, 5th edn, Prentice-Hall, 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, Prentice-Hall, Englewood Cliffs.
  • MATLAB, current version, Student Edition, CD and Users Guide.

Student workload requirements

Activity Hours
Assessments 20.00
Examinations 2.00
Private Study 150.00

Assessment details

Description Marks out of Wtg (%) Due Date Notes
ASSIGNMENT 1 100 10 27 Mar 2012
ASSIGNMENT 2 100 15 30 Apr 2012
ASSIGNMENT 3 100 15 28 May 2012
2HR RESTRICTED EXAM 100 60 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

  1. Attendance requirements:
    There are no attendance requirements for this course. However, it is the students' responsibility 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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, take an appropriate unmarked non-electronic 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.

  7. 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.

  8. 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

  1. 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.

  2. 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.