MATH5846
Introduction to Probability and
Stochastic Processes
Semester 1, 2014
CRICOS Provider No: 00098G
MATH5846 – Course Outline
Course Authority and lecturer: Dr Diana Combe
Email: [email protected]
Phone: 9385 7022
Office: RC-1032.
Consultation: Consultation times are by appointment. Please speak to the lecturer
in class, or send an email, to arrange a time.
Credit, Prerequisites, Exclusions: This course counts for 6 Units of Credit
(6UOC). There are no prerequisites or exclusions for this course.
Lectures: The lectures run in weeks 2-7 of the UNSW Semester 1, 2014. That is,
they start on Tuesday 11th March and finish on Thursday 17th April.
The class meets twice a week for three hours. In each 3 hour class meeting there
will be a couple of hours of lectures, a tutorial time and a short break.
Tuesday
5-8 pm
QUAD–G040
Thursday 5-8 pm
QUAD–G048
Course Overview
Probabilistic concepts are necessary to study various complex phenomena arising in
Engineering, Biology, Medicine and Economics. In this course we introduce basic
concepts which are needed to analyze such phenomena. In particular, we discuss
the concepts of random events, random variables, structures of dependence, computation of probabilities using the Central Limit Theorem, simple Markov chains and
Brownian motion. We may look at Poisson processes if time allows.
Assessment
Assessment in this course will consist of three assignments (10% each), a class test
(20%), and a final examination (50%).
Assessment criteria: For each assessment task, the main marking criteria will be
clear and logical presentation of correct solutions.
Assignments: There are three (written) assignments. These assignments are due
in at the start of the classes on each of Tuesday 25th March, Tuesday 1st April and
Thursday 17th April. Late assignments will not be accepted. Each assignment will
be available at least 10 days before it is due to be submitted.
Weighting: Each of the three assignments has a 10% weighting in your final mark.
Assignments give an opportunity for students to receive feedback on their progress
during the course, and to try their hand at more difficult problems requiring more
than one line of argument. Assignments also give an opportunity to introduce
aspects of the subject which are not explicitly covered in lectures.
Assignments must be YOUR OWN WORK, or severe penalties will be incurred.
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Class Test:
Duration: 1 hours duration, held during class, 5pm, Tuesday 8th April.
The test will be held at the start of the class time.
A mid-session test gives an opportunity for students to demonstrate their understanding of the first part of the course, and to receive feedback on the presentation
of their solutions in under examination conditions.
The class test will assess material from chapters 1 - 6. Further detail concerning the
mid-session test will be made available in lectures and on the MATH5846 web page,
closer to the time.
Weighting: 20% of your final mark.
Final Examination:
Duration: 2 hours duration, held on Thursday 24th April at 5pm to be held in
the Red Centre, level 4, RC-4082
Rationale: The final examination will assess student mastery of the the whole
course.
Weighting: 50% of your final mark.
Further details about the final examination will be available in class closer to the
time. Announcements will also be made on the MATH5846 web page.
Every class is different, and to accommodate this, some variation from the above
assessment schedule may be prudent. Hence the above schedule should be considered
as a guide only, as it may possibly not be strictly adhered to. In the case of assessment dates, no changes will be made without consultation with the class as well as
confirmation being posted as an announcement on the course web page.
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Schedule of assessment tasks and lecture chapters
Week beginning Lecture chapters
10th March
chapters 1 and 2
17th March
chapters 3 and 4
24th March
chapters 4 (cont)
and 5
31st March
chapter 6
7th April
chapter 7
14th April
chapter 8
21st April
no lectures
this week
Assessment due
Assessment weighting
Assignment 1 due at class
10%
5pm Tuesday 25th March
Assignment 2 due at class
10%
5pm Tuesday 1st April
1 hour class test
20%
5 pm Tuesday 8th April
Assignment 3 due at class
10%
5pm Thursday 17th April
2 hour final exam
50%
5pm Thursday 24th April
held in RC-4082
It is intended that the following topics will be covered in the given order. Sometimes
the particular chapters will not fit exactly into a particular week.
Chapter 1 – Probability: Experiments, axioms and basic results, conditional
probability, independence, Bayes’ Formula.
Chapter 2 – Random Variables: Definition, cumulative distribution function,
discrete and continuous random variables, expectations, moments, standard deviation, moment generating functions, Chebychev’s Inequality.
Chapter 3 – Common Distributions: Bernoulli, Binomial, Poisson, Geometric,
Hypergeometric, Uniform, Normal, Exponential, Gamma and Beta distributions.
Chapter 4 – Bivariate Distributions: Joint cdf, probability function and density function, conditional probability and density functions, conditional expected
value and variance, covariance and correlation, the bivariate normal distribution,
extension to n random variables.
Chapter 5 – Transformations: Linear transformations, probability integral transformations, bivariate transformations, sums of independent random variables.
Chapter 6 – Convergence of Random Variables: Convergence in probability,
weak law of large numbers, Central Limit Theorem, applications.
Chapter 7 – Markov chains.
Chapter 8 – Brownian motion.
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Additional resources and support
Exercises: Sets of exercises will be given out, and made available on the course web
page. These problems are for you to do to enhance mastery of the course. Some of
the problems will be done in lectures, but you will learn a lot more if you try some
of them beforehand.
Textbooks: Although there is no set text for this course, the following references
may prove useful. These books are available from the UNSW library, and are all
available from the main shelves as well as available for from the ‘High Use Collection’.
Mathematical Statistics with Applications, Sixth Edition, Duxbury Advanced Series,
Denis D Wackerly, William Mendenhall III & Richard L. Scheaffer.
Mathematical Statistics and Data Analysis, J.A. Rice.
Introduction to Probability Models, S. Ross
UNSW Moodle: The School of Mathematics and Statistics uses the Learning
Management System called Moodle. To log in to Moodle use your zID and zPass at
the following URL:
http://moodle.telt.unsw.edu.au
All course materials, including lecture notes, will be available on the MATH5846
homepage. You should check regularly for new materials.
Course Evaluation and Development
The School of Mathematics and Statistics evaluates each course each time it is
run. We carefully consider the student responses and their implications for course
development. It is common practice to discuss informally with students how the
course and their mastery of it are progressing.
Administrative matters
Additional Assessment and School Rules and Regulations: See the School
of Mathematics and Statistics web page for general policy on additional assessment,
and for fuller details of the general rules regarding attendance, release of marks,
special consideration etc.
http://www.maths.unsw.edu.au/currentstudents/assessment-policies
Plagiarism and academic honesty
Plagiarism is the presentation of the thoughts or work of another as one’s own. Issues
you must be aware of regarding plagiarism and the university’s policies on academic
honesty and plagiarism can be found at www.lc.unsw.edu.au/plagiarism
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