Unit convenor and teaching staff |
Unit convenor and teaching staff
Unit Convenor
Georgy Sofronov
Contact via georgy.sofronov@mq.edu.au
12 Wally's Walk (E7A), Room 535
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Credit points |
Credit points
3
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Prerequisites |
Prerequisites
STAT171 and (MATH133(P) or MATH136(P))
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Corequisites |
Corequisites
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Co-badged status |
Co-badged status
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Unit description |
Unit description
This unit is a mathematically-based introduction to probability theory. Emphasis is placed on the theoretical development of the subject matter. Students should be mathematically competent, especially in the areas of integration, differentiation and the summation of infinite series. Students who are not confident about their ability in these areas should consider enrolling in the more general unit, STAT273. Topics include: conditional probability; discrete and continuous random variables; transformations; convolutions; moments and moment generating functions; central limit theorem; sampling distributions; order statistics; and bivariate distributions.
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Information about important academic dates including deadlines for withdrawing from units are available at https://www.mq.edu.au/study/calendar-of-dates
On successful completion of this unit, you will be able to:
Name | Weighting | Hurdle | Due |
---|---|---|---|
Test | 10% | No | Week 7 |
Assignments | 30% | No | Week 4, 9, 12 |
Final examination | 60% | No | University Examination Period |
Due: Week 7
Weighting: 10%
There will be a mid-semester test of 50 minutes duration held during the first lecture of week 7. Students are permitted to take in to the test one sheet of A4 paper containing the student’s personal summary. One or both sides of the sheet may be used. The material thereon may be in the student’s own handwriting (scanned copies are not permitted) and not typed.
Due: Week 4, 9, 12
Weighting: 30%
There will be three assignments, the first one due in week 4, Assignment 2 due in week 9 and Assignment 3 due in week 12.
Assignment submission: Assignments are to be submitted to your tutor, in your tutorial in the week in which they are due. No extensions will be considered unless satisfactory documentation outlining illness or misadventure is submitted. In these special circumstances you may apply for special consideration via ask.mq.edu.au.
In the case of a late submission for an assignment, if no special consideration has been granted, 10% of the earned mark will be deducted for each day that an assignment is late, up to a maximum of 50%. After 5 days, counted including weekends and public holidays, a mark of 0% will be awarded. NOTE: It is not the intention of this late penalty policy to cause a student to fail the unit when they have submitted their assignment no more than 5 days after the due date and they would have otherwise passed. In this case, if deductions for late assignments result in the final unit mark for a student being less than 50, when otherwise it would have been 50 or greater, the student's final mark will be exactly 50.
Due: University Examination Period
Weighting: 60%
The duration of the final examination is three hours plus ten minutes’ reading time. An electronic calculator and two A4 sheets of paper (written on one or both sides) may be taken in to the exam room. All material thereon must be in the student's own handwriting (scanned copies are not permitted) and not typed.
You are expected to present yourself for examination at the time and place designated in the University examination timetable, which will be available at https://timetables.mq.edu.au.
Only documented illness or unavoidable disruption may be used as reasons for not sitting an examination at the designated time. In these circumstances you may wish to consider applying for special consideration via ask.mq.edu.au.
Information about the Special Consideration Policy is available at:
https://staff.mq.edu.au/work/strategy-planning-and-governance/university-policies-and-procedures/policies/special-consideration
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 the 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 Special Consideration Policy prior to submitting an application. You can check the supplementary exam information page on FSE101 in iLearn (bit.ly/FSESupp) for dates, and approved applicants will receive an individual notification one week prior to the exam with the exact date and time of their supplementary examination.
All unit materials, including administrative updates, lecture notes, tutorials and assignments, will be posted on the Unit website on iLearn. The web address is https://ilearn.mq.edu.au.
Students will attend three one-hour lectures and one one-hour tutorial per week. The notes shown in lectures will be available on iLearn before the lecture is given, but note that corrections may be made after the lecture. Tutorial exercises will be set weekly and will be available on iLearn before the tutorial. Students are expected to have attempted all questions before the tutorial. A plan of the topics to be covered is at the end of this document.
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)
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 print out your own copy and bring this to lectures.
None.
TOPIC |
MATERIAL COVERED |
1 |
Sample space, events. Axioms of probability, conditional probability. Bayes Theorem. Random variables and probability distributions. |
2 |
Discrete Distributions and their applications (Bernoulli, geometric, negative binomial, binomial, hypergeometric, multinomial). The Poisson process and the Poisson distribution. |
3 |
Continuous random variables and distributions with applications (uniform, exponential, triangular, normal, gamma, beta etc.). Discrete and continuous cumulative distribution functions. |
4 |
Expected values (discrete and continuous) and properties of the expectation operator. Measures of variation. |
5 |
Moments: raw and central. Interpretation of moments (skewness, kurtosis etc.). |
6 |
Sums of independent random variables. Discrete and continuous convolutions with applications. |
7 |
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. |
8 |
Probability generating functions and moment generating functions (raw and central) with properties and applications. The moment generating function of a sum of independent random variables. The uniqueness theorem. Characteristic functions. |
9 |
Chebyshev’s inequality. The central limit theorem and applications. |
10 |
Multivariate (particularly bivariate) random variable theory (continuous and discrete). Marginal and conditional distributions and expectations. Covariance and correlation. Compound distributions. |
11 |
Order statistics, specifically the distributions of the minimum, maximum and median. |
Macquarie University policies and procedures are accessible from Policy Central (https://staff.mq.edu.au/work/strategy-planning-and-governance/university-policies-and-procedures/policy-central). Students should be aware of the following policies in particular with regard to Learning and Teaching:
Undergraduate students seeking more policy resources can visit the Student Policy Gateway (https://students.mq.edu.au/support/study/student-policy-gateway). It is your one-stop-shop for the key policies you need to know about throughout your undergraduate student journey.
If you would like to see all the policies relevant to Learning and Teaching visit Policy Central (https://staff.mq.edu.au/work/strategy-planning-and-governance/university-policies-and-procedures/policy-central).
Macquarie University students have a responsibility to be familiar with the Student Code of Conduct: https://students.mq.edu.au/study/getting-started/student-conduct
Results shown in iLearn, 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.
Macquarie University provides a range of support services for students. For details, visit http://students.mq.edu.au/support/
Learning Skills (mq.edu.au/learningskills) provides academic writing resources and study strategies to improve your marks and take control of your study.
Students with a disability are encouraged to contact the Disability Service who can provide appropriate help with any issues that arise during their studies.
For all student enquiries, visit Student Connect at ask.mq.edu.au
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.
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