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STA2301 Distribution Theory

Semester 1, 2019 On-campus Toowoomba
Short Description: Distribution Theory
Units : 1
Faculty or Section : Faculty of Health, Engineering and Sciences
School or Department : School of Agric, Comp and Environ Sciences
Student contribution band : Band 2
ASCED code : 010103 - Statistics
Grading basis : Graded


Examiner: Taryn Axelsen


Pre-requisite: STA2300 and (MAT1102 or ENM1600)


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.


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.


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). (

Please contact us for alternative purchase options from USQ Bookshop. (

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.

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.
Hogg, RV, McKean, JW& Craig, AT 2018, Introduction to Mathematical Statistics, 8th edn, Pearson Education, Upper Saddle River, NJ.
Miller, I 2014, John E. Freund's mathematical statistics with applications, 8th edn, Pearson, Boston.
Rohatgi, V K and Saleh, A K Md E 2015, An Introduction to Probability and Statistics, 3rd edn, Wiley, New York.

Student workload expectations

Activity Hours
Assessments 22.00
Online 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 2019
ASSIGNMENT 2 100 15 30 Apr 2019
ASSIGNMENT 3 100 15 28 May 2019
2HR RESTRICTED EXAM 100 55 End S1 (see note 1)

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

Important assessment information

  1. Attendance requirements:
    It is the students' responsibility to participate appropriately in all activities 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.

  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:
    Students should refer to the Assessment Procedure (point 4.2.4)

  4. Requirements for student to be awarded a passing grade in the course:
    To be assured of receiving a passing grade a student must obtain at least 50% of the total weighted marks available for the course (i.e. the Primary Hurdle), and have satisfied the Secondary Hurdle (Supervised), i.e. the end of semester examination by achieving at least 40% of the weighted marks available for that assessment item.

    Supplementary assessment may be offered where a student has undertaken all of the required summative assessment items and has passed the Primary Hurdle but failed to satisfy the Secondary Hurdle (Supervised), or has satisfied the Secondary Hurdle (Supervised) but failed to achieve a passing Final Grade by 5% or less of the total weighted Marks.

    To be awarded a passing grade for a supplementary assessment item (if applicable), a student must achieve at least 50% of the available marks for the supplementary assessment item as per the Assessment Procedure (point 4.4.2).

  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

Other requirements

  1. Computer, e-mail and Internet access:
    Students are required to have access to a personal computer, e-mail capabilities and Internet access to UConnect. Current details of computer requirements can be found at

  2. Students can expect that questions in assessment items in this course may draw upon knowledge and skills that they can reasonably be expected to have acquired before enrolling in this course. This includes knowledge contained in pre-requisite courses and appropriate communication, information literacy, analytical, critical thinking, problem solving or numeracy skills. Students who do not possess such knowledge and skills should not expect the same grades as those students who do possess them.