MATHS 2103 - Probability & Statistics II

North Terrace Campus - Semester 1 - 2025

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.

Open All

Course Details

Course Code	MATHS 2103
Course	Probability & Statistics II
Coordinating Unit	Mathematical Sciences
Term	Semester 1
Level	Undergraduate
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
Assessment	Ongoing assessment, examination

Course Staff

Course Coordinator: Dr Stephen Crotty

Course Timetable

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

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.

最新糖心Vlog 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 Modes

This course relies on topic videos as the primary delivery mechanism for the material. Tutorials are the primary direct contact hours, during which students will both reinforce and employ the understanding obtained through lectures. Weekly quizzes provide regular opportunities for students to gauge their progress and understanding.

Workload

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

Activity	Quantity	Workload hours
Videos and study		88
Tutorials	11	33
Assignments	5	25
Online quizzes	12	12
Total		158

Learning Activities Summary

**Topics 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 distributions	Cumulative 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 variables	The 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.

Each tutorial, starting in week 2, will cover material from the previous week.

The 最新糖心Vlog'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	Summative	Examination period	50%	All
Assignments	Formative and summative	Weeks 3,5,7,9 and 11	20%	All
Mid-semester test	Formative and summative	Week 7	20%	All
Online quizzes	Formative and summative	Weeks 1-12	10%	All

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	4%
Assignment 2	Week 4	Week 5	4%
Assignment 3	Week 6	Week 7	4%
Assignment 4	Week 8	Week 9	4%
Assignment 5	Week 10	Week 11	4%

Submission

Assignments are submited electronically through MyUni. 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 .

Student Feedback

The 最新糖心Vlog 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 最新糖心Vlog 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
This section contains links to relevant assessment-related policies and guidelines - all university policies.
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.

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

Authorised by:	Deputy Vice-Chancellor and Vice-President (Academic)
Maintained by:	Course Outlines Administrator

最新糖心Vlog