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STAT394 – Probability, Random Processes and Statistics for Engineers

2017 – S1 Day

General Information

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Unit convenor and teaching staff Unit convenor and teaching staff Convenor
Barry Quinn
Contact via x6475
E7A TBA
Credit points Credit points
3
Prerequisites Prerequisites
6cp at 200 level including MATH235(P)
Corequisites Corequisites
Co-badged status Co-badged status
Unit description Unit description
This unit develops the probabilistic and statistical ideas needed to apply the theory of random processes to engineering fields such as signal processing and communications. Topics covered include probability, random variables, expectation, random processes, stationarity, ergodicity, spectral density, limit theorems, markov chains, estimation theory.

Important Academic Dates

Information about important academic dates including deadlines for withdrawing from units are available at http://students.mq.edu.au/student_admin/enrolmentguide/academicdates/

Learning Outcomes

  1. Understand and compute probabilities, conditional probabilities, random variables.
  2. Understand and work with probability density functions, expectations, moment generating functions.
  3. Be able to compute the joint distributions and expectations of functions of more than one random variable.
  4. Understand and use the concepts of hypothesis testing, probability of false alarm.
  5. Be able to compute the likelihood and maximum likelihood estimators.

Assessment Tasks

Name Weighting Hurdle Due
Assignment 1 10% Friday 17th March
Assignment 2 10% Friday 14th April
Assignment 3 10% Friday 2nd June
Tutorial Participation 10% Weeks 2 to 13
Class Test 10% 5th May
Final Examination 50% TBA

Assignment 1

Due: Friday 17th March
Weighting: 10%

Submit to Prof Barry Quinn by 3pm on the due date. There is no “group work” assessment in this unit. All work is to be the student’s own. No extensions will be granted.  Students who have not submitted the assignment prior to the deadline will be awarded a mark of 0 for the assignment, except for cases in which an application for disruption to studies is made and approved.


This Assessment Task relates to the following Learning Outcomes:
  • Understand and compute probabilities, conditional probabilities, random variables.
  • Understand and work with probability density functions, expectations, moment generating functions.

Assignment 2

Due: Friday 14th April
Weighting: 10%

Submit to Prof Barry Quinn by 3pm on the due date. There is no “group work” assessment in this unit. All work is to be the student’s own. No extensions will be granted.  Students who have not submitted the assignment prior to the deadline will be awarded a mark of 0 for the assignment, except for cases in which an application for disruption to studies is made and approved.


This Assessment Task relates to the following Learning Outcomes:
  • Understand and work with probability density functions, expectations, moment generating functions.
  • Be able to compute the joint distributions and expectations of functions of more than one random variable.

Assignment 3

Due: Friday 2nd June
Weighting: 10%

Submit to Prof Barry Quinn by 3pm on the due date. There is no “group work” assessment in this unit. All work is to be the student’s own. No extensions will be granted.  Students who have not submitted the assignment prior to the deadline will be awarded a mark of 0 for the assignment, except for cases in which an application for disruption to studies is made and approved.


This Assessment Task relates to the following Learning Outcomes:
  • Be able to compute the joint distributions and expectations of functions of more than one random variable.
  • Understand and use the concepts of hypothesis testing, probability of false alarm.
  • Be able to compute the likelihood and maximum likelihood estimators.

Tutorial Participation

Due: Weeks 2 to 13
Weighting: 10%

Students will contribute to discussions and hand in at least one handwritten page of tutorial problem solutions per tutorial.


This Assessment Task relates to the following Learning Outcomes:
  • Understand and compute probabilities, conditional probabilities, random variables.
  • Understand and work with probability density functions, expectations, moment generating functions.
  • Be able to compute the joint distributions and expectations of functions of more than one random variable.
  • Understand and use the concepts of hypothesis testing, probability of false alarm.
  • Be able to compute the likelihood and maximum likelihood estimators.

Class Test

Due: 5th May
Weighting: 10%

The first class test will take place during the 1pm Friday class on 5th May. It will take place under exam conditions. The test is 'closed book'. Students may take into the test TWO A4 pages of notes handwritten (not typed) on BOTH sides. Calculators may be used but must not be of the text/programmable type. Students who do not attend the test will be awarded a mark of 0, unless they apply for disruption to studies and this is approved.


This Assessment Task relates to the following Learning Outcomes:
  • Understand and compute probabilities, conditional probabilities, random variables.
  • Understand and work with probability density functions, expectations, moment generating functions.
  • Be able to compute the joint distributions and expectations of functions of more than one random variable.

Final Examination

Due: TBA
Weighting: 50%

The final Examination will be held during the mid-year Examination period. The final Examination is 3 hours long (with an additional 10 minutes’ reading time). It will cover all topics in the unit. The final examination is closed book. Students may take into the final Exam TWO A4 pages of notes handwritten (not typed) on BOTH sides. Calculators will be needed but must not be of the text/programmable type.

The only exception to not sitting an examination on the designated date is because of documented illness or unavoidable disruption. In these circumstances you may wish to consider applying for disruption to studies.

If you notify the University of your disruption to studies for your final examination, you must make yourself available for the week of July 24 – 28, 2017.  If you are not available at that time, there is no guarantee an additional examination time will be offered. Specific examination dates and times will be determined at a later date.


This Assessment Task relates to the following Learning Outcomes:
  • Understand and compute probabilities, conditional probabilities, random variables.
  • Understand and work with probability density functions, expectations, moment generating functions.
  • Be able to compute the joint distributions and expectations of functions of more than one random variable.
  • Understand and use the concepts of hypothesis testing, probability of false alarm.
  • Be able to compute the likelihood and maximum likelihood estimators.

Delivery and Resources

There are four contact hours per week, comprised of three lectures and one tutorial. Check the timetable for the times and locations of classes.

Please consult iLearn or the Unit webpage for details of consultation hours.

Unit Schedule

Topic 1 Probability, conditional probability, independence, mutually exclusive events
Topic 2 Random variables, distribution function, discrete and continuous random variables, expectation, moments, moment generating function
Topic 3 Bivariate cdf and pdf, independent rvs, transformations, sums of rvs, central limit theorem, conditional expectation, distributions derived from the normal
Topic 4 Unbiased estimation, likelihood function, maximum likelihood, Cramer-Rao lower bound, asymptotic behaviour
Topic 5 Simple and composite hypotheses, critical regions, Neyman-Pearson lemma, significance levels, power, false alarm rates
Topic 6 Inequalities, laws of large numbers, order statistics

 

Learning and Teaching Activities

Lecture

Three hours per week

Tutorial

One hour per week

Policies and Procedures

Macquarie University policies and procedures are accessible from Policy Central. Students should be aware of the following policies in particular with regard to Learning and Teaching:

Academic Honesty Policy http://mq.edu.au/policy/docs/academic_honesty/policy.html

Assessment Policy http://mq.edu.au/policy/docs/assessment/policy_2016.html

Grade Appeal Policy http://mq.edu.au/policy/docs/gradeappeal/policy.html

Complaint Management Procedure for Students and Members of the Public http://www.mq.edu.au/policy/docs/complaint_management/procedure.html​

Disruption to Studies Policy (in effect until Dec 4th, 2017): http://www.mq.edu.au/policy/docs/disruption_studies/policy.html

Special Consideration Policy (in effect from Dec 4th, 2017): https://staff.mq.edu.au/work/strategy-planning-and-governance/university-policies-and-procedures/policies/special-consideration

In addition, a number of other policies can be found in the Learning and Teaching Category of Policy Central.

Student Code of Conduct

Macquarie University students have a responsibility to be familiar with the Student Code of Conduct: https://students.mq.edu.au/support/student_conduct/

Results

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.

Student Support

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

Learning Skills

Learning Skills (mq.edu.au/learningskills) provides academic writing resources and study strategies to improve your marks and take control of your study.

Student Enquiry Service

For all student enquiries, visit Student Connect at ask.mq.edu.au

Equity Support

Students with a disability are encouraged to contact the Disability Service who can provide appropriate help with any issues that arise during their studies.

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.

Graduate Capabilities

Critical, Analytical and Integrative Thinking

We want our graduates to be capable of reasoning, questioning and analysing, and to integrate and synthesise learning and knowledge from a range of sources and environments; to be able to critique constraints, assumptions and limitations; to be able to think independently and systemically in relation to scholarly activity, in the workplace, and in the world. We want them to have a level of scientific and information technology literacy.

This graduate capability is supported by:

Learning outcomes

  • Understand and compute probabilities, conditional probabilities, random variables.
  • Understand and work with probability density functions, expectations, moment generating functions.
  • Be able to compute the joint distributions and expectations of functions of more than one random variable.
  • Understand and use the concepts of hypothesis testing, probability of false alarm.
  • Be able to compute the likelihood and maximum likelihood estimators.

Assessment tasks

  • Assignment 1
  • Assignment 2
  • Assignment 3
  • Tutorial Participation
  • Class Test
  • Final Examination

Learning and teaching activities

  • Three hours per week
  • One hour per week

Effective Communication

We want to develop in our students the ability to communicate and convey their views in forms effective with different audiences. We want our graduates to take with them the capability to read, listen, question, gather and evaluate information resources in a variety of formats, assess, write clearly, speak effectively, and to use visual communication and communication technologies as appropriate.

This graduate capability is supported by:

Assessment tasks

  • Tutorial Participation
  • Class Test

Learning and teaching activities

  • Three hours per week
  • One hour per week

Discipline Specific Knowledge and Skills

Our graduates will take with them the intellectual development, depth and breadth of knowledge, scholarly understanding, and specific subject content in their chosen fields to make them competent and confident in their subject or profession. They will be able to demonstrate, where relevant, professional technical competence and meet professional standards. They will be able to articulate the structure of knowledge of their discipline, be able to adapt discipline-specific knowledge to novel situations, and be able to contribute from their discipline to inter-disciplinary solutions to problems.

This graduate capability is supported by:

Learning outcomes

  • Understand and compute probabilities, conditional probabilities, random variables.
  • Understand and work with probability density functions, expectations, moment generating functions.
  • Be able to compute the joint distributions and expectations of functions of more than one random variable.
  • Understand and use the concepts of hypothesis testing, probability of false alarm.
  • Be able to compute the likelihood and maximum likelihood estimators.

Assessment tasks

  • Assignment 1
  • Assignment 2
  • Assignment 3
  • Tutorial Participation
  • Class Test
  • Final Examination

Learning and teaching activities

  • Three hours per week
  • One hour per week

Problem Solving and Research Capability

Our graduates should be capable of researching; of analysing, and interpreting and assessing data and information in various forms; of drawing connections across fields of knowledge; and they should be able to relate their knowledge to complex situations at work or in the world, in order to diagnose and solve problems. We want them to have the confidence to take the initiative in doing so, within an awareness of their own limitations.

This graduate capability is supported by:

Learning outcomes

  • Understand and compute probabilities, conditional probabilities, random variables.
  • Understand and work with probability density functions, expectations, moment generating functions.
  • Be able to compute the joint distributions and expectations of functions of more than one random variable.
  • Understand and use the concepts of hypothesis testing, probability of false alarm.
  • Be able to compute the likelihood and maximum likelihood estimators.

Assessment tasks

  • Assignment 1
  • Assignment 2
  • Assignment 3
  • Tutorial Participation
  • Class Test
  • Final Examination

Learning and teaching activities

  • Three hours per week
  • One hour per week

Textbooks and other reference material

A textbook that has been used in the past is

Richard H. Williams, Probability, Statistics, and Random Processes for Engineers, Cengage Learning, 2003.

Other good references are

A. Leon-Garcia, Probability, Statistics, and Random Processes for Electrical Engineering, 3 ed. Upper Saddle River, New Jersey: Prentice-Hall, 2008

and

A. Papoulis, Probability, Random Variables, and Stochastic Processes. New York: McGraw-Hill, 2002.

There are many introductory mathematical statistics and/or random (stochastic) processes books, and many are suitable references.

The notes in iLearn will be fairly exhaustive, and will be put up approximately one week in advance of their delivery, or earlier.

Changes since First Published

Date Description
28/02/2017 Added Unit Schedule
02/02/2017 Added the requested info on supplementary exams - Anne Macmillan 27 January.