**Winter 2007**

**Course meets:**

Tuesday and Thursday 4:10-5:30, 1060 East Hall.

**Instructor:**
Sergey Fomin, 2858 East Hall, 764-6297,
fomin@umich.edu

**Office hours:**
Tuesday 5:40-7:00 and Thursday 11:40-1:00 in 2858 East Hall.

**Grader:** Paul Siegel,
siegelp@umich.edu.

**Course homepage:** http://www.math.lsa.umich.edu/~fomin/525w07.html

**Text (required):**
Geoffrey Grimmett and David Stirzaker,
*Probability and Random Processes*,
3rd edition, Oxford University Press, 2001.

Where can I buy this textbook?

**Supplementary texts (not required):**

Geoffrey Grimmett and David Stirzaker,
*One Thousand Exercises in Probability*,
2nd edition, Oxford University Press, 2001.

Sheldon Ross,
*Introduction to Probability Models*,
8th/9th edition, Academic Press, 2002/2006.

Sheldon Ross,
*A First Course in Probability*,
6th/7th edition, Prentice-Hall, 2002/2006.

**Prerequisites:** Math 450 or Math 451 (preferred) and some exposure to
elementary probability and combinatorics.

**From departmental course description:**

This introductory course in probability theory is more theoretical than
Math 425, and requires a stronger mathematical background. No measure
theory is assumed.
Topics include: probability spaces, discrete and continuous random
variables, joint distributions and conditional expectations,
characteristic functions, central limit theorem, random walk.

**Grade** will be based on two 1.5-hour midterm exams, 30% each;
40% homework and quizzes.

Your lowest homework/quiz score will be dropped.

This course will **not** be graded on a curve, i.e., there are not a set
number of each grade to be given out.
Every student with the total score of 90% (resp., 80%, 70%, 60%)
is guaranteed the final grade of A (resp., B or higher, C or higher, D
or higher).

The midterm exams are held in class. **No makeups** will be given.

Exams are closed book, closed notebook.

You will be allowed to bring a
3-by-5 index card to the 1st midterm, and two such cards to the 2nd
midterm.

**First midterm**: March 6.

**Second midterm**: April 17.

**Exam preparation**: see below for practice problems and other
potentially useful links

C.M.Grinstead and J.L.Snell,

J.Walrand,

**Other online resources**:

Virtual Laboratories in Probability and Statistics

List of web resources in statistics and probability

Basic counting techniques

Proof of Stirling's formula

*January 11*:
1.2.3, 1.3.3, 1.3.4, 1.4.3, 1.4.7, 1.8.12,
1.8.22, 1.8.24, 1.8.28

*January 18*:
1.5.7, 1.5.9, 1.7.1, 1.7.3, 1.7.5, 1.8.20, 1.8.21, 1.8.35, 1.8.39

*January 25*:
2.7.15, 3.1.1(a,b,d), 3.1.3, 3.2.1, 3.2.2(a,b,c), 3.2.4(a)

*February 1*:
3.3.2, 3.5.1, 3.11.7, 3.11.11, 3.11.13(b), 3.11.21(a), 3.11.24

*February 8*:
3.3.3, 3.4.3, 3.4.8, 3.6.8, 3.11.8, 3.11.12, 3.11.16

*February 15*:
3.6.3, 3.7.4, 3.7.5(b), 3.11.4, 3.11.6(b)

*March 8, 15*:
4.1.1(a), 4.1.2, 4.2.2, 4.3.3 (*r*=1),
4.13.14, 5.8.9(a), 5.10.1(a),
5.12.25(a), 5.12.33(a)

*March 22*:
4.4.3, 4.4.5, 4.7.3, 4.7.4(a), 4.7.13
(1^{st} part), 5.10.2, 5.12.5 (1^{st} part)

*March 29*:
4.5.4, 4.7.7(c), 4.7.11, 4.8.3, 4.14.7,
4.14.54, 4.14.55 (1^{st} part)

*April 5*:
4.6.1, 4.6.4, 4.6.9, 4.7.8, 4.7.10

The exam will cover

**Preparing for the Second Exam**:

The exam will roughly cover **Sections 4.1-4.8, 5.7-5.10** in
Grimmett and Stirzaker.
Besides the practice problems listed above,
I recommend problems 29-39, 41, 43-45, 48-49, 52-53 in this set of exercises.
The answers can be found here.
This web page
has some complete solutions, and a couple of old exams.