MATHS 7103 - Probability & Statistics
North Terrace Campus - Semester 1 - 2020
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General Course Information
Course Details
Course Code MATHS 7103 Course Probability & Statistics Coordinating Unit Mathematical Sciences Term Semester 1 Level Postgraduate Coursework Location/s North Terrace Campus Units 3 Contact Up to 3.5 hours per week Available for Study Abroad and Exchange Y Prerequisites MATHS 1012 or MATHS 1004 or MATHS 7027 Assumed Knowledge MATHS 1012 or MATHS 7027 Assessment Ongoing assessment, exam Course Staff
Course Coordinator: Dr Jono Tuke
Course Timetable
The full timetable of all activities for this course can be accessed from .
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Learning Outcomes
Course Learning Outcomes
Students who successfully complete this course should be able to demonstrate understanding of :
1 basic probability axioms and rules and the moments of discrete and continous random variables as well as be familiar with common named discrete and continous random variables. 2 how to derive the probability density function of transformations of random variables and use these techniques to generate data from various distributions. 3 how to calculate probabilities, and derive the marginal and conditional distributions of bivariate random variables. 4 discrete time Markov chains and methods of finding the equilibrium probability distributions. 5 how to calculate probabilities of absorption and expected hitting times for discrete time Markov chains with absorbing states. 6 how to translate real-world problems into probability models. 7 how to read and annotate an outline of a proof and be able to write a logical proof of a statement.
University Graduate Attributes
This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:
University Graduate Attribute Course Learning Outcome(s) Deep discipline knowledge
- informed and infused by cutting edge research, scaffolded throughout their program of studies
- acquired from personal interaction with research active educators, from year 1
- accredited or validated against national or international standards (for relevant programs)
1,2,3,4,5,6,7 Critical thinking and problem solving
- steeped in research methods and rigor
- based on empirical evidence and the scientific approach to knowledge development
- demonstrated through appropriate and relevant assessment
5,6,7 Teamwork and communication skills
- developed from, with, and via the SGDE
- honed through assessment and practice throughout the program of studies
- encouraged and valued in all aspects of learning
4,5 Career and leadership readiness
- technology savvy
- professional and, where relevant, fully accredited
- forward thinking and well informed
- tested and validated by work based experiences
6 Self-awareness and emotional intelligence
- a capacity for self-reflection and a willingness to engage in self-appraisal
- open to objective and constructive feedback from supervisors and peers
- able to negotiate difficult social situations, defuse conflict and engage positively in purposeful debate
4,5 -
Learning Resources
Required Resources
None.Recommended Resources
There are many good books on probability and statistics in the Barr Smith Library, with the following texts being recommended for this course.
1 "Mathematical Statistics with Applications" by Wackerly, Mendenhall and Schaeffer (Duxbury 2008).
2. "Introduction to Stochastic Models" by Roe Goodman (2nd edition, Dover, 2006).
3. "Introduction to Probability Models" by Sheldon Ross (Academic Press, 2010).
4. "Mathematical Statistics and Data Analysis" by John Rice (Duxbury Press, 2006).
For other texts on probability and statistics, try browsing books with call numbers beginning with 519.2.Online Learning
A semblance of the course notes will available online for those who wish to download and print prior to attending lectures. The format (either as two or one slide per page) is the same as the presentation slides used in the lectures, with room for you to annotate during lectures.
Recordings of lectures will also be available online immediately following each lecture for those who are unable to attend due to other commitments and for revision purposes.
All assignments, tutorials, handouts and solutions where appropriate will also be available online progressively as the course ensues. -
Learning & Teaching Activities
Learning & Teaching Modes
The lecturer will guide the students through the material presented in this course in a total of 36 lectures. Downloading and prereading the online notes will enable the students to more actively engage the material and interact during lectures. Students are expected to attend all lectures, but these will be recorded and made available online for those who are occasionally absent.
There are six tutorials during the presentation of the course that are held fortnightly, where groups of students will present solutions to assigned questions at the beginning of their tutorial. There will be sufficient time for active discussion on these questions where necessary and for the consideration of other questions.
In alternative weeks to the tutorial sessions, students will have assignment questions to submit for assessment which will be returned within two weeks, giving students direct feedback on their understanding of the course material. This material will contribute towards the students' final assessment as noted in the assessment summary.Workload
The information below is provided as a guide to assist students in engaging appropriately with the course requirements.
Activity Quantity Workload hours Lectures 36 101 Tutorials 6 18 Assignments 5 25 Online quizzes 12 12 Total 158 Learning Activities Summary
Lecture Schedule Week 1 Discrete random variables Probability mass function, expectation and variance. Bernoulli distribution, Geometric distribution, Binomial distribution. Derivation of mean and variance. Week 2 Discrete random variables Sampling with and without replacement. Hypergeometric distribution and Poisson distribution. Derivation of the Poisson distribution as limiting form of Binomial. Derivation of mean and variance. Week 3 Discrete random variables Bounding probabilities, tail sum formula, Markov’s inequality and Chebyshev’s inequality. Probability generating functions and moment generating functions. Week 4 Continuous random variables Probability density function, cumulative distribution function, expectation, mean and variance. Moment generating functions and uniqueness theorem. Chebyshev’s inequality. Week 5 Continuous random variables The uniform distribution on (a, b), the normal distribution. Mean and variance of the normal distribution. The Cauchy distribution. The exponential distribution, moments, memoryless property, hazard function. Week 6 Continuous random variables Gamma distribution, moments, Chi-square distribution. Point processes, the Poisson process, derivation of the Poisson and exponential distributions. Week 7 Transformation of random variables
and bivariate distributionsCumulative distribution function method for finding the distribution of a function of random variable. The transformation rule. Discrete bivariate distributions, marginal and conditional distributions, the trinomial distribution and multinomial distribution. Week 8 Bivariate distributions Continuous bivariate distributions, marginal and conditional distributions, independence of random variables. Covariance and correlation. Mean and variance of linear combination of two random variables. The joint Moment generating function (MGF) and MGF of the sum. Week 9 Bivariate distributions and
independent random variablesThe bivariate normal distribution, marginal and conditional distributions, conditional expectation and variance, joint MGF and marginal MGF. Linear combinations of independent random variables. Means and variances. Sequences of independent random variables and the weak law of large numbers. The central limit theorem, normal approximation to the binomial distribution. Week 10 Discrete time Markov chains Definition of a Markov chain and probability transition matrices. Equilibrium behaviour of Markov chains: computer demonstration and ergodic, limiting and stationary interpretations. Week 11 Discrete time Markov chains Methods for solving Equilibrium Equations using probability generating functions and partial balance. Week 12 Discrete time Markov chains Definition of absorbing Markov chains, structural results, hitting probabilities and expected hitting times. Review.
The first tutorial in week 2 covers material from week 1 and other material that should be considered revision. Tutorials in weeks 4,6,8,10 and 12 cover the material of the previous two weeks.Small Group Discovery Experience
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Assessment
The University's policy on Assessment for Coursework Programs is based on the following four principles:
- Assessment must encourage and reinforce learning.
- Assessment must enable robust and fair judgements about student performance.
- Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
- Assessment must maintain academic standards.
Assessment Summary
Assessment task Task type When due Weighting Learning outcomes Examination (3 hours) Summative Examination period 60% All Assignments Formative and summative Weeks 3,5,7,9 and 11 25% All Mid-semester test Formative and summative Week 7 10% All Online quizzes Formative and summative Weeks 1-12 5% All Note that the examination for MATHS 7103 is of 3 hours duration.
Due to the current COVID-19 situation modified arrangements have been made to assessments to facilitate remote learning and teaching. Assessment details provided here reflect recent updates.
Assignments 25%
Online Quizzes 5%
Timed online test 20%
Online exam 50%Assessment Related Requirements
An aggregate score of 50% is required in order to pass this course.Assessment Detail
Assessment task Set Due Weighting Assignment 1 Week 2 Week 3 5% Assignment 2 Week 4 Week 5 5% Assignment 3 Week 6 Week 7 5% Assignment 4 Week 8 Week 9 5% Assignment 5 Week 10 Week 11 5% Submission
Assignments must be submitted on time with a signed assessment cover sheet attached to the assignment. Late assignments will not be accepted. Assignments will be returned within two weeks. Students may be excused from an assignment for medical or compassionate reasons. In such cases, documentation is required and the lecturer must be notified as soon as possible before the fact.Course Grading
Grades for your performance in this course will be awarded in accordance with the following scheme:
M10 (Coursework Mark Scheme) Grade Mark Description FNS Fail No Submission F 1-49 Fail P 50-64 Pass C 65-74 Credit D 75-84 Distinction HD 85-100 High Distinction CN Continuing NFE No Formal Examination RP Result Pending Further details of the grades/results can be obtained from Examinations.
Grade Descriptors are available which provide a general guide to the standard of work that is expected at each grade level. More information at Assessment for Coursework Programs.
Final results for this course will be made available through .
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Student Feedback
The University places a high priority on approaches to learning and teaching that enhance the student experience. Feedback is sought from students in a variety of ways including on-going engagement with staff, the use of online discussion boards and the use of Student Experience of Learning and Teaching (SELT) surveys as well as GOS surveys and Program reviews.
SELTs are an important source of information to inform individual teaching practice, decisions about teaching duties, and course and program curriculum design. They enable the University to assess how effectively its learning environments and teaching practices facilitate student engagement and learning outcomes. Under the current SELT Policy (http://www.adelaide.edu.au/policies/101/) course SELTs are mandated and must be conducted at the conclusion of each term/semester/trimester for every course offering. Feedback on issues raised through course SELT surveys is made available to enrolled students through various resources (e.g. MyUni). In addition aggregated course SELT data is available.
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Student Support
- Academic Integrity for Students
- Academic Support with Maths
- Academic Support with writing and study skills
- Careers Services
- Library Services for Students
- LinkedIn Learning
- Student Life Counselling Support - Personal counselling for issues affecting study
- Students with a Disability - Alternative academic arrangements
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Policies & Guidelines
This section contains links to relevant assessment-related policies and guidelines - all university policies.
- Academic Credit Arrangements Policy
- Academic Integrity Policy
- Academic Progress by Coursework Students Policy
- Assessment for Coursework Programs Policy
- Copyright Compliance Policy
- Coursework Academic Programs Policy
- Intellectual Property Policy
- IT Acceptable Use and Security Policy
- Modified Arrangements for Coursework Assessment Policy
- Reasonable Adjustments to Learning, Teaching & Assessment for Students with a Disability Policy
- Student Experience of Learning and Teaching Policy
- Student Grievance Resolution Process
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Fraud Awareness
Students are reminded that in order to maintain the academic integrity of all programs and courses, the university has a zero-tolerance approach to students offering money or significant value goods or services to any staff member who is involved in their teaching or assessment. Students offering lecturers or tutors or professional staff anything more than a small token of appreciation is totally unacceptable, in any circumstances. Staff members are obliged to report all such incidents to their supervisor/manager, who will refer them for action under the university's student鈥檚 disciplinary procedures.
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