| Semester 1, 2020 On-campus Toowoomba | |
| Short Description: | Distribution Theory |
| Units : | 1 |
| Faculty or Section : | Faculty of Health, Engineering and Sciences |
| School or Department : | School of Sciences |
| Student contribution band : | Band 2 |
| ASCED code : | 010103 - Statistics |
| Grading basis : | Graded |
Staffing
Examiner:
Requisites
Pre-requisite: STA2300 or equivalent and (MAT1102 or ENM1600)
Rationale
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.
Synopsis
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.
Objectives
On successful completion of this course students will be able to:
- Define probability concepts and identify properties of commonly used distributions.
- Derive probability distributions and functions of random variables.
- Evaluate the appropriateness of particular probability models to a variety of contexts.
- Apply a statistical package to evaluate the probability of suitably defined events and related applications.
- Communicate probability and probability distributional results using appropriate terminology for expert and non-expert audiences.
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 (unless otherwise stated). (https://omnia.usq.edu.au/textbooks/?year=2020&sem=01&subject1=STA2301)
Please for alternative purchase options from USQ Bookshop. (https://omnia.usq.edu.au/info/contact/)
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 精东传媒appDesk.
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 精东传媒app | 98.00 |
| Tutorials | 26.00 |
Assessment details
| Description | Marks out of | Wtg (%) | Due Date | Notes |
|---|---|---|---|---|
| ASSIGNMENT 1 | 100 | 15 | 24 Mar 2020 | |
| ASSIGNMENT 2 | 100 | 15 | 28 Apr 2020 | |
| ASSIGNMENT 3 | 100 | 15 | 22 May 2020 | |
| Take Home Exam | 100 | 55 | End S1 | (see note 1) |
Notes
- This will be an open examination. Students will be provided further instruction regarding the exam by their course examiner via 精东传媒appDesk. The examination date will be available via UConnect when the official examination timetable has been released.
Important assessment information
-
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. -
Requirements for students to complete each assessment item satisfactorily:
Due to COVID-19 the requirements for S1 2020 are: To satisfactorily complete an individual assessment item a student must achieve at least 50% of the marks for that item.
Requirements after S1 2020:
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:
Students should refer to the Assessment Procedure (point 4.2.4) -
Requirements for student to be awarded a passing grade in the course:
Due to COVID-19 the requirements for S1 2020 are: To be assured of receiving a passing grade a student must achieve at least 50% of the total weighted marks available for the course.
Requirements after S1 2020:
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). -
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:
Due to COVID-19 the requirements for S1 2020 are: An Open Examination is one in which candidates may have access to any printed or written material and a calculator during the examination
Requirements after S1 2020:
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:
Due to COVID-19 the requirements for S1 2020 are: The details regarding deferred/supplementary examinations will be communicated at a later date
Requirements after S1 2020:
Any Deferred or Supplementary examinations for this course will be held during the next examination period. -
精东传媒app Student Policies:
Students should read the USQ policies: Definitions, Assessment and Student Academic Misconduct to avoid actions which might contravene 精东传媒app policies and practices. These policies can be found at .
Other requirements
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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 . -
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.