STA2301 Distribution Theory
|Semester 1, 2013 On-campus Toowoomba|
|Faculty or Section :||Faculty of Sciences|
|School or Department :||Maths and Computing|
|Version produced :||8 March 2014|
Examiner: Shahjahan Khan
Moderator: Christine McDonald
Pre-requisite: STA2300 and MAT1102
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.
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.
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.
|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=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.
Berry, DA & Lindgren, BW 1996, Statistics: Theory and 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.
R package – free download from internet.
Student workload requirements
|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)|
- Examination dates will be available during the Semester. Please refer to Examination timetable when published.
Important assessment information
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.
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.
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.
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.