Students

STAT7310 – Statistical Theory

2022 – Session 1, In person-scheduled-weekday, North Ryde

General Information

Download as PDF
Unit convenor and teaching staff Unit convenor and teaching staff Lead Unit Convenor/Lecturer
Georgy Sofronov
georgy.sofronov@mq.edu.au
Contact via Email
please refer to iLearn
Second Unit Convenor/Lecturer
Benoit Liquet-Weiland
benoit.liquet-weiland@mq.edu.au
Contact via Email
please refer to iLearn
Credit points Credit points
10
Prerequisites Prerequisites
Admission to MRes
Corequisites Corequisites
Co-badged status Co-badged status
STAT8310
Unit description Unit description

This unit introduces the foundation concepts of probability and statistics. The unit develops probability concepts, including random variables and distributions, independence, joint and conditional distributions, expectations, generating functions, distributions of sums of independent random variables and the Central Limit Theorem. The principles of statistical inference are discussed with a particular focus on point estimators, confidence intervals and hypothesis testing.

Important Academic Dates

Information about important academic dates including deadlines for withdrawing from units are available at https://www.mq.edu.au/study/calendar-of-dates

Learning Outcomes

On successful completion of this unit, you will be able to:

  • ULO1: Apply concepts related to probability and statistics including random variables and distributions, independence, joint and conditional distributions, expectations, generating functions, distributions of sums of independent random variables and the Central Limit Theorem.
  • ULO2: Summarise data using appropriate statistical analysis, descriptive statistics and graphical presentation.
  • ULO3: Evaluate the appropriateness of a variety of statistical models/methods for various types of data, apply them, and interpret the results.
  • ULO4: Apply concepts related to statistical inference including point estimators, confidence intervals and hypothesis testing.

General Assessment Information

The online quiz, test and exam must be undertaken at the time indicated in the unit guide or on iLearn. Should these activities be missed due to illness or misadventure, students may apply for special consideration.

ASSIGNMENT SUBMISSION: Assignment submission will be online through the iLearn page.

Submit assignments online via the appropriate assignment link on the iLearn page. A personalised cover sheet is not required with online submissions. Read the submission statement carefully before accepting it as there are substantial penalties for making a false declaration.

  • Assignment submission is via iLearn. You should upload this as a single scanned PDF file.
  • Please note the quick guide on how to upload your assignments provided on the iLearn page.
  • Please make sure that each page in your uploaded assignment corresponds to only one A4 page (do not upload an A3 page worth of content as an A4 page in landscape). If you are using an app like Clear Scanner, please make sure that the photos you are using are clear and shadow-free.
  • It is your responsibility to make sure your assignment submission is legible.
  • If there are technical obstructions to your submitting online, please email us to let us know.

You may submit as often as required prior to the due date/time. The assisgnment must be submitted by 5:00 pm on its due date. Please note that each submission will completely replace any previous submissions. It is in your interests to make frequent submissions of your partially completed work as insurance against technical or other problems near the submission deadline.

LATE SUBMISSION OF WORK:  All assessment tasks must be submitted by the official due date and time. Should these assessments be missed due to illness or misadventure, students should apply for special consideration. In the case of a late submission for a non-timed assessment (e.g. an assignment), if special consideration has NOT been granted, a consistent penalty will be applied for the late submission as follows. A 12-hour grace period will be given after which the following deductions will be applied to the awarded assessment mark; 12 to 24 hours late = 10% deduction; for each day thereafter, an additional 10% per day or part thereof will be applied until five days beyond the due date. After this time (including weekends and/or public holidays), a mark of zero (0) will be given. Timed assessment tasks (e.g. iLean quiz, test, examination) do not fall under these rules.

FINAL EXAM POLICY: It is Macquarie University policy not to set early examinations for individuals or groups of students. All students are expected to ensure that they are available until the end of the teaching semester, that is, the final day of the official examination period. The only excuse for not sitting an examination at the designated time is because of documented illness or unavoidable disruption. In these special circumstances, you may apply for special consideration via ask.mq.edu.au.

If you receive special consideration for the final exam, a supplementary exam will be scheduled in the interval between the regular exam period and the start of the next session. By making a special consideration application for the final exam you are declaring yourself available for a resit during this supplementary examination period and will not be eligible for a second special consideration approval based on pre-existing commitments. Please ensure you are familiar with the policy prior to submitting an application.

Assessment Tasks

Name Weighting Hurdle Due
iLearn Quiz 5% No Week 5
Test 20% No Week 7
Assignment 15% No Week 11
Final Examination 60% No University Examination Period

iLearn Quiz

Assessment Type 1: Quiz/Test
Indicative Time on Task 2: 1 hours
Due: Week 5
Weighting: 5%

 

iLearn Quiz

 
On successful completion you will be able to:
  • Apply concepts related to probability and statistics including random variables and distributions, independence, joint and conditional distributions, expectations, generating functions, distributions of sums of independent random variables and the Central Limit Theorem.

Test

Assessment Type 1: Quiz/Test
Indicative Time on Task 2: 1 hours
Due: Week 7
Weighting: 20%

 

Mid-Semester Class Test

 
On successful completion you will be able to:
  • Apply concepts related to probability and statistics including random variables and distributions, independence, joint and conditional distributions, expectations, generating functions, distributions of sums of independent random variables and the Central Limit Theorem.

Assignment

Assessment Type 1: Quantitative analysis task
Indicative Time on Task 2: 8 hours
Due: Week 11
Weighting: 15%

 

Assignment

 
On successful completion you will be able to:
  • Summarise data using appropriate statistical analysis, descriptive statistics and graphical presentation.
  • Evaluate the appropriateness of a variety of statistical models/methods for various types of data, apply them, and interpret the results.
  • Apply concepts related to statistical inference including point estimators, confidence intervals and hypothesis testing.

Final Examination

Assessment Type 1: Examination
Indicative Time on Task 2: 3 hours
Due: University Examination Period
Weighting: 60%

 

Invigilated Final Examination

 
On successful completion you will be able to:
  • Apply concepts related to probability and statistics including random variables and distributions, independence, joint and conditional distributions, expectations, generating functions, distributions of sums of independent random variables and the Central Limit Theorem.
  • Summarise data using appropriate statistical analysis, descriptive statistics and graphical presentation.
  • Evaluate the appropriateness of a variety of statistical models/methods for various types of data, apply them, and interpret the results.
  • Apply concepts related to statistical inference including point estimators, confidence intervals and hypothesis testing.

1 If you need help with your assignment, please contact:

  • the academic teaching staff in your unit for guidance in understanding or completing this type of assessment
  • the Writing Centre for academic skills support.

2 Indicative time-on-task is an estimate of the time required for completion of the assessment task and is subject to individual variation

Delivery and Resources

Technologies used and required

The unit is delivered by lectures (2 hours per week, starting in Week 1) and SGTAs (1 hour per week, starting in Week 2). All teaching material will be available on iLearn. 

SGTA exercises will be available from iLearn prior to the SGTA. Students are expected to have attempted these prior to the SGTA. Solutions will be explained, with emphasis on any area students had trouble with. At the end of the week, these solutions will then be placed on iLearn. The web address is https://ilearn.mq.edu.au.

The R software (freely available online) will be used in the unit. Students need to practice how to use the software and be expected to use R for the assignment. Students should also note that the test and the final examination may contain inline R codes and output that students need to interpret to answer the questions.

Required and Recommended texts and/or materials

There is no required textbook for this unit. Students may benefit from having access to the following background reference for additional reading and problems:

“Mathematical Statistics with Applications” W Mendenhall, D Wackerly and R Scheaffer (6th or 7th edition) - library call number is QA276.M426.

The following books may also be useful background references:

ROSS, S. A First Course in Probability (QA273.R83)

SCHEAFFER, R. L. Introduction to Probability and Its Applications (QA273.S357)

SMITH, P. J. Into Statistics (QA276.S615)

FREUND, J. E. Mathematical Statistics (QA276.F692)

HOEL, P. Introduction to Mathematical Statistics (QA276.H57)

HOGG, R.V. & TANIS, E.A. Probability and Statistical Inference (QA273.H694)

LARSON, H. Introduction to Probability Theory and Statistical Inference (QA273.L352)

SPIEGEL, M.R., SRINIVASAN, J. & SCHILLER, J.J. Schaum's outline of theory and problems of probability and statistics (QA273.25.S64)

WALPOLE, R.E. & MYERS, R.H. Probability and Statistics for Engineers and Scientists (TA340.W35)

HOGG, R.V. & CRAIG, A.T. Introduction to Mathematical Statistics (QA276.H59)

CASELLA, G. & BERGER, R.L. Statistical Inference (QA276.C37) 

At least one copy of each of these is available in the Library, and extra copies may be available on the shelves for borrowing purposes.

It should be understood that there are variations in notation (and even in definition) from one reference book to another, and that the lecture material alone defines recommended notation. Note that all lecture notes will be available in pdf form on the Unit website on iLearn before the lecture. You are required to bring a hard or soft copy of the lecture notes to lectures.

Unit Schedule

TOPIC

MATERIAL COVERED

1

Sample space, events. Axioms of probability, conditional probability. Bayes Theorem.

2

Random variables and probability distributions. Standard discrete and continuous distributions and their key characteristics. The Poisson process.

3

Expected values (discrete and continuous) and their properties. Measures of variation. Quantiles. Moments (raw and central). Interpretation of moments (skewness, kurtosis etc.).

4

Sums of independent random variables. Discrete and continuous convolutions with applications. Transformations (monotonic and non-monotonic) of continuous random variables. Transformation of a continuous random variable to one with a uniform distribution, with applications to simulation.

5

Probability generating functions and moment generating functions with properties and applications. The moment generating function of a sum of independent random variables. The Central Limit Theorem and applications.

6

Multivariate (particularly bivariate) random variable theory (continuous and discrete). Marginal and conditional distributions and expectations. Covariance and correlation. 

7

Exploratory data analysis including measures of association and principal component analysis.

8

Random sampling and sampling distributions.

9

Point estimators and their properties. MLEs and asymptotic results and bootstrapping.

10

Interval estimators, their properties.

11

Hypothesis testing, including likelihood ratios and goodness of fit.

Policies and Procedures

Macquarie University policies and procedures are accessible from Policy Central (https://policies.mq.edu.au). Students should be aware of the following policies in particular with regard to Learning and Teaching:

Students seeking more policy resources can visit Student Policies (https://students.mq.edu.au/support/study/policies). It is your one-stop-shop for the key policies you need to know about throughout your undergraduate student journey.

To find other policies relating to Teaching and Learning, visit Policy Central (https://policies.mq.edu.au) and use the search tool.

Student Code of Conduct

Macquarie University students have a responsibility to be familiar with the Student Code of Conduct: https://students.mq.edu.au/admin/other-resources/student-conduct

Results

Results published on platform other than eStudent, (eg. iLearn, Coursera etc.) or released directly by your Unit Convenor, are not confirmed as they are subject to final approval by the University. Once approved, final results will be sent to your student email address and will be made available in eStudent. For more information visit ask.mq.edu.au or if you are a Global MBA student contact globalmba.support@mq.edu.au

Academic Integrity

At Macquarie, we believe academic integrity – honesty, respect, trust, responsibility, fairness and courage – is at the core of learning, teaching and research. We recognise that meeting the expectations required to complete your assessments can be challenging. So, we offer you a range of resources and services to help you reach your potential, including free online writing and maths support, academic skills development and wellbeing consultations.

Student Support

Macquarie University provides a range of support services for students. For details, visit http://students.mq.edu.au/support/

The Writing Centre

The Writing Centre provides resources to develop your English language proficiency, academic writing, and communication skills.

The Library provides online and face to face support to help you find and use relevant information resources. 

Student Services and Support

Macquarie University offers a range of Student Support Services including:

Student Enquiries

Got a question? Ask us via AskMQ, or contact Service Connect.

IT Help

For help with University computer systems and technology, visit http://www.mq.edu.au/about_us/offices_and_units/information_technology/help/. 

When using the University's IT, you must adhere to the Acceptable Use of IT Resources Policy. The policy applies to all who connect to the MQ network including students.