MATHS 7103 - Probability & Statistics PG

North Terrace Campus - Trimester 2 - 2022

Probability theory is the branch of mathematics that deals with modelling uncertainty. It is important because of its direct application in areas such as genetics, finance and telecommunications. It also forms the fundamental basis for many other areas in the mathematical sciences including statistics, modern optimisation methods and risk modelling. This course provides an introduction to probability theory, random variables and Markov processes. Topics covered are: probability axioms, conditional probability; Bayes' theorem; discrete random variables, moments, bounding probabilities, probability generating functions, standard discrete distributions; continuous random variables, uniform, normal, Cauchy, exponential, gamma and chi-square distributions, transformations, the Poisson process; bivariate distributions, marginal and conditional distributions, independence, covariance and correlation, linear combinations of two random variables, bivariate normal distribution; sequences of independent random variables, the weak law of large numbers, the central limit theorem; definition and properties of a Markov chain and probability transition matrices; methods for solving equilibrium equations, absorbing Markov chains.

  • General Course Information
    Course Details
    Course Code MATHS 7103
    Course Probability & Statistics PG
    Coordinating Unit School of Mathematical Sciences
    Term Trimester 2
    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 7027
    Course Description Probability theory is the branch of mathematics that deals with modelling uncertainty. It is important because of its direct application in areas such as genetics, finance and telecommunications. It also forms the fundamental basis for many other areas in the mathematical sciences including statistics, modern optimisation methods and risk modelling. This course provides an introduction to probability theory, random variables and Markov processes.

    Topics covered are: probability axioms, conditional probability; Bayes' theorem; discrete random variables, moments, bounding probabilities, probability generating functions, standard discrete distributions; continuous random variables, uniform, normal, Cauchy, exponential, gamma and chi-square distributions, transformations, the Poisson process; bivariate distributions, marginal and conditional distributions, independence, covariance and correlation, linear combinations of two random variables, bivariate normal distribution; sequences of independent random variables, the weak law of large numbers, the central limit theorem; definition and properties of a Markov chain and probability transition matrices; methods for solving equilibrium equations, absorbing Markov chains.
    Course Staff

    Course Coordinator: Dr Shenal Dedduwakumara

    Course Timetable

    The full timetable of all activities for this course can be accessed from Course Planner.

  • Learning Outcomes
    Course Learning Outcomes
    On successful completion of this course you will be able to:
    1 Demonstrate an understanding of basic probability axioms; the rules and moments of discrete and continuous random variables.
    2 Derive the probability density function (PDF) of transformations of random variables and generate data from various distributions.
    3 Calculate probabilities and derive the marginal and conditional distributions of bivariate random variables.
    4 Find equilibrium probablity distributions.
    5 Calculate probabilities of absorption and expected hitting times for discrete time Markov chains with absorbing states.


    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)

    Attribute 1: Deep discipline knowledge and intellectual breadth

    Graduates have comprehensive knowledge and understanding of their subject area, the ability to engage with different traditions of thought, and the ability to apply their knowledge in practice including in multi-disciplinary or multi-professional contexts.

    1,2,3,4,5,6,7

    Attribute 2: Creative and critical thinking, and problem solving

    Graduates are effective problems-solvers, able to apply critical, creative and evidence-based thinking to conceive innovative responses to future challenges.

    5,6,7

    Attribute 3: Teamwork and communication skills

    Graduates convey ideas and information effectively to a range of audiences for a variety of purposes and contribute in a positive and collaborative manner to achieving common goals.

    4,5

    Attribute 4: Professionalism and leadership readiness

    Graduates engage in professional behaviour and have the potential to be entrepreneurial and take leadership roles in their chosen occupations or careers and communities.

    6

    Attribute 8: Self-awareness and emotional intelligence

    Graduates are self-aware and reflective; they are flexible and resilient and have the capacity to accept and give constructive feedback; they act with integrity and take responsibility for their actions.

    4,5
  • Learning & Teaching Activities
    Learning & Teaching Modes
    This course is delivered in a semester, trimester and intensive format, although enrolment options may be limited by availability.

    This course offers opportunities for you to learn through blended learning approaches, meaning some of the learning is done autonomously online and some of the learning is done through face-to-face engagement. This blended approach is used to create a rich scaffolded and supportive learning experience.

    Workload

    The information below is provided as a guide to assist students in engaging appropriately with the course requirements.

    This is a 3-unit course. In the semester or trimester format, you are expected to allocate the following study time to fully meet the Course Learning Outcomes (CLOs) for this course. Please note that students work at different paces, so this indicates the approximate time required to complete this course.

    Learning Activity Hours/Week Duration Total
    Online learning activities 1 hour 12 weeks 12 hours
    Face-to-face learning activities 3 hours 12 weeks 36 hours
    Indpendent study 4 hours 12 weeks 48 hours
    Assessment tasks 5 hours 12 weeks 60 hours
    Expected total student workload 156 hours
    Learning Activities Summary
    You will be required to complete the online learning activities available on MyUni prior to regular face-to-face learning sessions. Throughout these autonomous tasks, you will have time to process new concepts and build foundational knowledge around them. In the face-to-face sessions, you will get a chance to apply that learning to build new skills and address real-world problems.

    Learning activities, both online and face-to-face, are scaffolding to the learning builds throughout the course. Through this learning experience, you will be asked to draw on a range of lower-order and higher-order thinking skills.

  • Assessment

    The University's policy on Assessment for Coursework Programs is based on the following four principles:

    1. Assessment must encourage and reinforce learning.
    2. Assessment must enable robust and fair judgements about student performance.
    3. Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
    4. Assessment must maintain academic standards.

    Assessment Summary

    No information currently available.

    Assessment Detail
    Full descriptions of the assessment tasks and associated grading rubrics are in the Assignments space on the MyUni course site. You will have opportunities to get further clarification on assessment tasks as needed.
    Submission
    Unless otherwise specified, submit all of your assessments to the Assignments space in the MyUni course site for this course. For written assessments, your submissions will go through Turnitin to check for originality. Make sure your submissions adhere to the University of Adelaide Academic Integrity policies.
    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 Access Adelaide.

  • 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.

  • Student Support
  • Policies & Guidelines
  • 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’s disciplinary procedures.

The University of Adelaide is committed to regular reviews of the courses and programs it offers to students. The University of Adelaide therefore reserves the right to discontinue or vary programs and courses without notice. Please read the important information contained in the disclaimer.