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STAT273 – Introduction to Probability

2017 – S1 Day

General Information

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Unit convenor and teaching staff Unit convenor and teaching staff Unit Convenor
Georgy Sofronov
Contact via georgy.sofronov@mq.edu.au
Friday, 12-2pm
Credit points Credit points
3
Prerequisites Prerequisites
(STAT170(P) or STAT171 or STAT150) and ((HSC Mathematics Band 2 or Extension 1 or Extension 2) or 3cp from MATH111-MATH339)
Corequisites Corequisites
Co-badged status Co-badged status
This unit is co-taught with STAT683.
Unit description Unit description
This unit consolidates and expands upon the material on probability introduced in statistics units at 100 level. The emphasis is on the understanding of probability concepts and their application. Examples are taken from areas as diverse as biology, medicine, finance, sport, and the social and physical sciences. Topics include: the foundations of probability; probability models and their properties; some commonly used statistical distributions; relationships and association between variables; distribution of functions of random variables and sample statistics; approximations including the central limit theorem; and an introduction to the behaviour of random processes. Simulation is used to demonstrate many of these concepts.

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. Be able to describe a probabilistic model for an experiment, calculate probability and conditional probability of an event. Understand the independence of events.
  2. Understand the difference between discrete and continuous random variables.
  3. For discrete or continuous random variables be able to calculate probabilities of events, their expected values and variances. Graph the probability distributions or probability density functions and the cumulative distribution functions. Using moment generating functions for finding of moments of random variables. Generate random numbers from distributions and use these numbers for solving probability problems.
  4. Understand a bivariate probability distribution, joint, marginal, conditional probabilities and covariance. Understand a bivariate Normal distribution.
  5. Be familiar with limit theorems: the Law of Large Numbers (LLN) and the Central Limit Theorem (CLT).
  6. Be able to generate random data. Be able to organise and summarise any random data. Determine whether a particular model fits random data.
  7. Understand a Markov Chain (MC), a stationary distribution of MC and interpretation of MCs with absorbing states.

General Assessment Information

On-time submission of the assessment tasks is compulsory. Late submission will not be accepted unless satisfactory documentation outlining illness or misadventure is submitted via ask.mq.edu.au. Information about the Disruption to Studies policy and procedure is available at:

http://students.mq.edu.au/student_admin/exams/disruption_to_studies/

http://www.mq.edu.au/policy/docs/disruption_studies/policy.html

http://www.mq.edu.au/policy/docs/disruption_studies/procedure.html

Assessment Tasks

Name Weighting Hurdle Due
Tutorial Participation 10% Weeks 2 to 13
Test 1 10% Week 4 lecture
Assignment 1 10% Week 7
Test 2 10% Week 10 lecture
Assignment 2 10% Week 12
Final Examination 50% University Examination Period

Tutorial Participation

Due: Weeks 2 to 13
Weighting: 10%

To obtain full marks, students must participate in every tutorial. Participation and engagement in the class activities will be assessed by the tutor via rosters and observation of students' work during classes. The tutorial participation marks are equally weighted and together worth 10% of the unit assessment.


This Assessment Task relates to the following Learning Outcomes:
  • Be able to describe a probabilistic model for an experiment, calculate probability and conditional probability of an event. Understand the independence of events.
  • Understand the difference between discrete and continuous random variables.
  • For discrete or continuous random variables be able to calculate probabilities of events, their expected values and variances. Graph the probability distributions or probability density functions and the cumulative distribution functions. Using moment generating functions for finding of moments of random variables. Generate random numbers from distributions and use these numbers for solving probability problems.
  • Be familiar with limit theorems: the Law of Large Numbers (LLN) and the Central Limit Theorem (CLT).
  • Be able to generate random data. Be able to organise and summarise any random data. Determine whether a particular model fits random data.

Test 1

Due: Week 4 lecture
Weighting: 10%

You are allowed to bring in one A4 page of handwritten notes, written on both sides. All necessary statistical tables and formulae will be provided.

An electronic calculator is essential. Non-programmable calculators with no text-retrieval capacity are allowed in the tests or exam. 


This Assessment Task relates to the following Learning Outcomes:
  • Be able to describe a probabilistic model for an experiment, calculate probability and conditional probability of an event. Understand the independence of events.
  • Understand the difference between discrete and continuous random variables.
  • For discrete or continuous random variables be able to calculate probabilities of events, their expected values and variances. Graph the probability distributions or probability density functions and the cumulative distribution functions. Using moment generating functions for finding of moments of random variables. Generate random numbers from distributions and use these numbers for solving probability problems.

Assignment 1

Due: Week 7
Weighting: 10%

Students will be given one week to complete the assignment. 


This Assessment Task relates to the following Learning Outcomes:
  • Be able to describe a probabilistic model for an experiment, calculate probability and conditional probability of an event. Understand the independence of events.
  • Understand the difference between discrete and continuous random variables.
  • For discrete or continuous random variables be able to calculate probabilities of events, their expected values and variances. Graph the probability distributions or probability density functions and the cumulative distribution functions. Using moment generating functions for finding of moments of random variables. Generate random numbers from distributions and use these numbers for solving probability problems.
  • Be familiar with limit theorems: the Law of Large Numbers (LLN) and the Central Limit Theorem (CLT).
  • Be able to generate random data. Be able to organise and summarise any random data. Determine whether a particular model fits random data.

Test 2

Due: Week 10 lecture
Weighting: 10%

You are allowed to bring in one A4 page of handwritten notes, written on both sides. All necessary statistical tables and formulae will be provided. An electronic calculator is essential. Non-programmable calculators with no text-retrieval capacity are allowed in the tests or exam. 


This Assessment Task relates to the following Learning Outcomes:
  • Be able to describe a probabilistic model for an experiment, calculate probability and conditional probability of an event. Understand the independence of events.
  • Understand the difference between discrete and continuous random variables.
  • For discrete or continuous random variables be able to calculate probabilities of events, their expected values and variances. Graph the probability distributions or probability density functions and the cumulative distribution functions. Using moment generating functions for finding of moments of random variables. Generate random numbers from distributions and use these numbers for solving probability problems.
  • Be familiar with limit theorems: the Law of Large Numbers (LLN) and the Central Limit Theorem (CLT).

Assignment 2

Due: Week 12
Weighting: 10%

Students will be given one week to complete the assignment


This Assessment Task relates to the following Learning Outcomes:
  • Be able to describe a probabilistic model for an experiment, calculate probability and conditional probability of an event. Understand the independence of events.
  • Understand the difference between discrete and continuous random variables.
  • For discrete or continuous random variables be able to calculate probabilities of events, their expected values and variances. Graph the probability distributions or probability density functions and the cumulative distribution functions. Using moment generating functions for finding of moments of random variables. Generate random numbers from distributions and use these numbers for solving probability problems.
  • Understand a bivariate probability distribution, joint, marginal, conditional probabilities and covariance. Understand a bivariate Normal distribution.
  • Be familiar with limit theorems: the Law of Large Numbers (LLN) and the Central Limit Theorem (CLT).
  • Be able to generate random data. Be able to organise and summarise any random data. Determine whether a particular model fits random data.

Final Examination

Due: University Examination Period
Weighting: 50%

The examination will be of 3 hours duration with 10 minutes reading time.

For the Final examination you are allowed to bring in one A4 page of handwritten notes, written on both sides. All necessary statistical tables and formulae will be provided.

An electronic calculator is essential and will be required. Non-programmable calculators with no text-retrieval capacity are allowed in the tests or exam. 

You are expected to present yourself for examination at the time and place designated in the University Examination Timetable. The timetable will be available in Draft form approximately eight weeks before the commencement of the examinations and in Final form approximately four weeks before the commencement of the examinations (http://www.exams.mq.edu.au)

If you apply for Disruption to Study 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:
  • Be able to describe a probabilistic model for an experiment, calculate probability and conditional probability of an event. Understand the independence of events.
  • Understand the difference between discrete and continuous random variables.
  • For discrete or continuous random variables be able to calculate probabilities of events, their expected values and variances. Graph the probability distributions or probability density functions and the cumulative distribution functions. Using moment generating functions for finding of moments of random variables. Generate random numbers from distributions and use these numbers for solving probability problems.
  • Understand a bivariate probability distribution, joint, marginal, conditional probabilities and covariance. Understand a bivariate Normal distribution.
  • Be familiar with limit theorems: the Law of Large Numbers (LLN) and the Central Limit Theorem (CLT).
  • Be able to generate random data. Be able to organise and summarise any random data. Determine whether a particular model fits random data.
  • Understand a Markov Chain (MC), a stationary distribution of MC and interpretation of MCs with absorbing states.

Delivery and Resources

Classes 

STAT273 is delivered by lectures and tutorials.

The timetable for classes can be found on the University web site at:

http://www.timetables.mq.edu.au

Required and Recommended Texts and/or Materials 

There is no set textbook for this subject. Lecture notes will be available from iLearn at least the night before the lecture. Students should read the lecture notes before the lecture. All teaching materials will be available via iLearn.

References that may be useful

  • Wackerly, D. D., Mendenhall, W., Scheaffer, R. L. Mathematical Statistics with Applications (4th,5th, 6th or 7th Editions)
  • Ross, S. A First Course in Probability, Pearson (5th, 6th, 7th, 9th or 9th Editions)
  • Ward, M. D. and Gundlach, E. (2016) Introduction to Probability, W. H. Freeman and Company
  • Kinney, J.J. (1997) Probability - An Introduction with Statistical Applications, John Wiley and Sons
  • Scheaffer R.L. (1994) Introduction to Probability and Its Applications, (2nd Edition) Duxbury Press
  • Sincich,T., Levine, D.M., Stephan, D. (1999) Practical Statistics by Example using Microsoft Excel

Technology Used and Required

iLearn

There will be an iLearn site for this unit where weekly information, online discussions, lecture notes, iLectures, practice exercises and solutions will be posted.

Students are required to login to iLearn using their Student ID Number and myMQ Portal Password (note, information about how to get hold of your password is provided by the weblink http://ilearn.mq.edu.au).

The website for the iLearn login is https://ilearn.mq.edu.au/login/MQ/. You can only access the material if you are enrolled in the unit.

Software

We will be using Microsoft Office for Windows (especially Excel), R and Wolfram Alpha, freely available online.

Audio/Video recordings of lectures will be available on iLearn soon after the lecture is delivered.

Course notes are available on iLearn before the lecture. Students should familiarise themselves with the notes before the lecture and bring a copy (in paper or electronic form) to class.

Teaching and Learning Strategy 

Lectures

Lectures begin in Week 1.  STAT273 students should attend 3 hours per week. The lecture notes will be available on iLearn before the lecture.

Tutorials

Tutorials begin in Week 2 and are based on work from the previous week’s lecture. The aim of tutorials is to apply techniques learnt in lectures to solve problems using a statistical  package. The material is available on iLearn.

Additional Exercises

Additional exercises may also be made available on iLearn. It is expected that students will attempt all questions. The exercises will not be discussed during the tutorial, although some may be discussed during  the lectures. A solution will be made available on the website.

Unit Schedule

 

 

 WEEK

LECTURE TOPIC

W1

Experiments, sample spaces, Probability Rules, Permutations and Combination

W2

Conditional Probability. Independence, BayesTheorem

W3

Random Variables. Probability Functions, Discrete Probability Distributions, Cumulative Distribution functions, Expected value and Variance. Moments.

W4

Important Discrete Distributions: Bernoulli, Binomial, Geometric and Poisson

W5

Moment generating functions. More Discrete Distributions: Negative Binomial and Hypergeometric.

W6

Introduction to Continuous random variables. Cumulative distribution function.

W7

ContinuouDistributions: UniformExponential.

 

Mid-semester break

W8

Normal distribution.

W9

Continuous Distributions: Gamma and Beta Distributions. Chebyshev’s Theorem.

W10

Sampling Distributions.

W11

Joint Distributions: Discrete and Continuous cases. 

W12

Introduction to Markov Chains. States, Transition probabilities, State vectors, Equilibrium, Absorbing States

W13

Revision

 

 

 

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

  • Be able to describe a probabilistic model for an experiment, calculate probability and conditional probability of an event. Understand the independence of events.
  • Understand the difference between discrete and continuous random variables.
  • For discrete or continuous random variables be able to calculate probabilities of events, their expected values and variances. Graph the probability distributions or probability density functions and the cumulative distribution functions. Using moment generating functions for finding of moments of random variables. Generate random numbers from distributions and use these numbers for solving probability problems.
  • Understand a Markov Chain (MC), a stationary distribution of MC and interpretation of MCs with absorbing states.

Assessment tasks

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

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

  • Be able to describe a probabilistic model for an experiment, calculate probability and conditional probability of an event. Understand the independence of events.
  • Understand the difference between discrete and continuous random variables.
  • For discrete or continuous random variables be able to calculate probabilities of events, their expected values and variances. Graph the probability distributions or probability density functions and the cumulative distribution functions. Using moment generating functions for finding of moments of random variables. Generate random numbers from distributions and use these numbers for solving probability problems.
  • Understand a bivariate probability distribution, joint, marginal, conditional probabilities and covariance. Understand a bivariate Normal distribution.
  • Be familiar with limit theorems: the Law of Large Numbers (LLN) and the Central Limit Theorem (CLT).
  • Be able to generate random data. Be able to organise and summarise any random data. Determine whether a particular model fits random data.
  • Understand a Markov Chain (MC), a stationary distribution of MC and interpretation of MCs with absorbing states.

Assessment tasks

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

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 outcome

  • Be able to generate random data. Be able to organise and summarise any random data. Determine whether a particular model fits random data.

Assessment tasks

  • Tutorial Participation
  • Assignment 1
  • Assignment 2
  • Final Examination