**FINAL EXAM INFORMATION:**

Announcements:

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.

**Instructor:**
Hanna Jankowski

**E-mail:** hanna[at]stat.washington.edu

Please include "[491]" (using square brackets) in the subjects of
your e-mails; this'll help me separate if from my other, mostly junk,
mail. Also, please send only plain text messages, no html.

**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.

**Bonus Work:**

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.

- The tests are all closed book tests. You will probably need a calculator - only non-programmable calculators are allowed.

- There will be no make-up tests scheduled. In case of illness supported by medical documentation, your grade will be based on your other grades, pro-rated accordingly.

- Course work will be handed back during lectures. If you
disagree with the mark you have received, you should submit a
request for regrading in writing to the instructor within
*three days*of when the work was returned.

- You are free to discuss your homework assignments with others, in fact, I would encourage you to do so. However, you must write up your own solutions. I cannot stress this last part enough: not only is the right thing to do, but it's also how you learn the material. The assignments are due at the beginning of the class on the due dates. I do not accept late assignments.

- Attendance at all lectures is very important.

- The best way to learn mathematics is to do mathematics. Make sure you keep up with the non-credit practice problems. Come see me if you have troubles. Understanding the lectures and working through the assignments and practice problems is the key to your success in this course.

- If you have any concerns/suggestions etc., please let me know. This is what I'm here for.

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**Practice** (non-credit - do not hand these
in) **problems**:

Review

Random Walk

Markov Chains 1

Markov Chains 2

Markov Chains 3 , with some answers.

MCMC and Poisson Process

CTMC

BM, CPP, and Martingales