FINAL EXAM INFORMATION:
Here are the summary notes. Last update: Dec.4th.
Let me know if you see some typos.
In previous probability courses (most likely 394/395), you learned about random variables as useful tools for modelling the random phenomena in the world. You also looked at joint behaviour of two or more random variables. In this class we will study a particular extension of this: the behaviour of random variables as they evolve in time. This type of analysis is of great use in many fields: from finance (stock prices) to biology (spread of an epidemic). Time-permitting, we will look at many accessible examples of stochastic processes: random walks, Markov chains, MCMC, (compound) Poisson process, birth-death chains, Brownian motion, branching processes, queueing systems...
The official prerequisite of this course is at least a 2.0 in MATH/STAT 394 and 395. We will also make use of quite a bit of calculus and matrix algebra.
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Office Hours: Every Wednesday and Friday, beginning September 29th, 3-4 pm, in McCarty Hall Library.
If you cannot make it to my office hours, please schedule an appointment. All appointments will take place in my office, Padelford B-220.
Lectures will be held in BLM 414.
The main reference for this course will be the lectures. As an additional reference text I have chosen Probability and Random Processes, by Geoffrey Grimmett and David Stirzaker, 3rd Edition. However, this is not a required text.
There is a copy of this text available (soon) for
short-term loan from the Mathematics Research Library in
Padelford Hall C-306. I have also requested that the following texts be
placed on reserve there.
Introduction to Probability Models by Sheldon Ross
An Introduction to Stochastic Modeling by Taylor and Karlin
Stochastic Modeling of Scientific Data by Peter Guttorp
There will be 4-6 assignments, roughly bi-weekly, two term tests and a final in this course. The assignments will be posted below, and will be worth 25% of your final grade. Note: I will sometimes pick some problems from the practice exercises and put them on your assignment - don't let this confuse you...
Assignment 1 Due: Friday, October 13th. With solutions.
Assignment 2. Due: Wednesday, October 25th. With solutions. Don't mock the typesetting - I didn't have time to fix it.
Assignment 3 . Due: Monday, November 13th. With solutions. [Typo corrected November 14th, 2pm]
Assignment 4 . Due: Friday, December 8th. With solutions [small typo for 4a fixed Dec.11].
Note: all assignments are due at the beginning of each lecture. There are no exceptions. I do not accept late assignments.
Term test 1: Friday, October 27th, 20%
Term test 2: Friday, November 17th, 20%
Final: December 14th, 8:30-10:20am, 35%
The tests will be held in Thomson 125.
Note: the exam will not be held in the same room as the lectures. This will be announced beforehand.
You will have the opportunity to earn bonus marks (up to a maximum of 5%) by presenting a problem, chosen by me, to the class. Interested students should let me know asap, as I have to limit the number of presentations per lecture to one. In lieu of a presentation, you may also choose to do a computer programming assignment. Again, please let me know asap if you're interested.
We have covered the following sections/topics:
Week 0 :
Practice (non-credit - do not hand these
Markov Chains 1
Markov Chains 2
Markov Chains 3 , with some answers.
MCMC and Poisson Process
BM, CPP, and Martingales