Math/Stats 425, Section 1, Fall 2003. Syllabus.
Monday, 10:00-11:00 AM, Room 1084 East Hall

Final exam is as scheduled by the Registrar, that is,
Wednesday, December 17, 4:00 - 6:00 PM.
The room is Dennison 260 (next to East Hall).

``Can't wait!"

Problem and Review Sessions:
Thursday, December 11, 2003: 1:00 - 2:00 PM, 1084 East Hall.
Monday, December 15, 2003: 1:30 - 2:30 PM, 1084 East Hall.

Instructor: Dan Burns

Office: 5834 East Hall

Phone: 763-0152

E-mail: dburns@umich.edu

This is the home page for our section. This page is an update of the syllabus/homework assignment webpage from last semester, together with a couple of links (see below) that may prove useful over the course of the term. For your convenience, here is the first day handout summarizing the course.

Written assignment for a given week usually due that Friday, but check the assignments themselves below.

There will be no group assignments for Fall, 2003.

Midterm exams are in class exams, Friday, October 3 and Friday, November 7. These exams will be in our usual classroom. Since the class is followed by another class in the same room, these exams will be 50 minutes long, exactly.

The Term Paper can be substituted for the second midterm exam. Here is a list of suggested topics from past classes, which needs to be updated because there are more possible topics I can suggest now. You are strongly encouraged to take advantage of this option.

Some Web Links for the Course:


Kyle Siegrist's online textbook and Java applets of probability experiments.
Don't use this site if you are not using a browser with up-to-date Java readers; the applets will crash an old browser.

The Dartmouth probability project "Chance" and their online textbook, "Introduction to Probability", by Grinstead and Snell.

The Writing Supplement:

If you are interested in taking the writing supplement to fulfill your LSA junior/senior
level writing requirement in the disciplines, send me an e-mail right away.

Schedule of HW Assignments and Exams:

Click on a section subject for a relevant link, if available.

September 3-5 Read: Ross, sections 2.1-2.5 (read examples 5a-5i first time through, others later) Basic definitions and examples. How do we model randomness? Frequentist approach; models and sample spaces.
September 8-12 Read: Ross, sections 1.1-4.
Write: Ch. 2, probs. #4, 7, 15, 28, 33. 		Counting (Combinatorics) Useful for evaluating probabilities with finite numbers of outcomes.
September 15-19 Read: Ross, sections 1.4-5, 3.1-3.2.
Write: Ch. 1, probs. #15, 21, 22, 28, 29, 31;
Ch. 2, probs. #39, 46, 52. 		More counting;
conditional probability. 		Multinomials ("many-sided coins").
Multi-stage experiments, later outcomes conditioned on previous outcomes.
September
22-26 		Read: Ross, sections 3.1-3.4.
Write: Ch. 3, probs. 6,7,8,12,24,53,62.
(Link is to written solutions for the highlighted problems.) 		Conditional probability; independence; Bayes's theorem. Some of the biggest concepts of the term!
September 28
- October 3 		Read: Ross, sections 3.5; 4.1-3.
(first reading of Ch. 4)
Suggested Problems for Exam prep:
Ch. 1 ST #2,4,6,10
Ch. 2 ST #2,4,7,11
Ch. 3 ST #3,8,12,19
ST = Self-Test problems
(NOT collected; save for exam study) 		Random variable, discrete RV, expectation. Random variable:
another big concept for us. Just a glimpse before
the first exam.
October
6 - 10 		Read: Ross, sections 4.1 - 4.7
Write: Ch. 4, probs. #13, 21, 23, 26, 43, 51.
Variance;
Bernoulli, binomial
and Poisson RVs. 		Variance (and its square root,
the standard deviation)
is everywhere important in statistics.
October
15 - 17 		Read: Ross, sections 4.8-9;
start 5.1-3.
Write: Ch. 4, probs. #48, 50, 53, 58. 		Examples of discrete RVs;
beginnings of continuous RVs. 		Beginnings of continuous probability;
now we have to use calculus as much
as combinatorics and counting.
October
20 - 24 		Read: Ross, sections 5.1-5, 5.7.
Write: Ch. 5, probs. #3, 4, 9, 10, 26, 31.
 Examples of continuous RVs;
beginnings of normal RVs,
DeMoivre's Theorem.
Waiting times and exponential RV's. 		Big topic: normal RV.
NB: Gil Stendig points out that problem #9 refers back to example 4b of Chapter 4, not 5b.
Thanks, Gil!

Refresh: two dimensional domains of integration; change of variables in integrals!
October
27 - 31 		Read: Ross, sections 5.6-7, 6.1-3
Write: Ch. 5, problems 34, 35, 39, 40; Ch. 6, probs. 2, 6. 		Hazard Rate functions;
change of RV's;
Gamma distribution, log-normal distribution. 		Hazard rate functions a point of view in insurance and risk analysis;
change of RV's enable random number generators to simulate general probability distributions;
log-normal distribution used in finance to model markets.

Sums are important for the
Central Limit Theorem and
Laws of Large Numbers.
November
3 - 7 		Read: Ross, Chapter 6.4 - 6.5.
No written problems collected this week; prepare for second mid-term. 		Jointly distributed RV's;
independence of RV's;
sums of RV's;
two dimensional events.
N.B.: We did not treat Proposition 3.2 of section 6.3 in class, but it is quite important.
Please have a look at it! 		Second MT
Friday, November 7:
Ross, Chapters 4, 5 and 6.1-3.

Some selected "Self-Test" Problems for Preparation:
Chap. 4: 3, 6 (long!), 8, 9, 13, 19;
Chap. 5: 1, 6, 8, 13, 15, 18.
Chap. 6: 1.
November
10 - 14 		Read: Ross, Chapter
6.4 - 6.7; skip 6.8.
Write: Ch. 6, #6, 9, 15, 17, 32 (see Prop. 3.2), 42.
Conditional distributions,
discrete and continuous cases;
functions of (several joint) RV's. 		Functions of RV's
are important for simulating experiments with standard pseudo-random number generators.
November
17 - 21 		Read: Ross, Ch. 6.6 - 6.7, 7.1 - 7.3,
skip sec. 7.2.1 & 7.2.2.
Write: Ch. 6, #39, 40, 45
Ch. 7, #8, 14, 18.
Order statistics.
Expectation, variance
and covariance
of joint RV's. 		``Order statistics" (6.6) important in statistics.
The important new idea here is the covariance.
November
24 - 26 		Read: Ross, Ch. 7.4 - 7.5, 7.7.
skip 7.6 & 7.8.
Write: Ch. 7, #21, 46, 47, 53, 55, 65.
Due: Monday, Dec. 1.

Happy Thanksgiving!

 Conditional expectation.
Prediction, ``multivariate" normals, and the
background to Laws of Large Numbers. 		Big week: the first three topics very important in applications, statistics; LLN begins to justify the ill-defined but popular ``law of averages".
December
1 - 5
Read: Ross, Ch. 8.1 - 8.4.
Here are some suggested problems we could go over before the exam:
Ch. 8, #3, 4, 6, 11, 14, 18, 20.
Central Limit
Theorem (CLT),
Strong Law of Large
Numbers (SLLN). 		Term ends with a bang:
two biggest results of the semester.
December
8 - 10
Read: Ross, Ch. 8.3, 8.4.
No written problems
due this week.
Here are some suggested problems we could go over before the exam, however:
Ch. 8, #3, 4, 6, 11, 14, 18, 20.

Term projects due:
December 11.

 Finish CLT, SLLN.
Summary and review for final.
 Prepare your questions for review, as well as requests for posting solutions.

Downloadable Group Problem Sets and Schedule of Group HW Assignments:

Click on a section subject for a relevant link, if available.

GPS #1
Now includes solutions! 		Problems on basic probability modeling
and conditional probability. 		Due: Wednesday, February 12, 2003.
GPS #2
Now contains (some) solutions! 		Expectation and continuous RV's Due: Wednesday, March 19, 2003.
GPS #3
Now contains solutions! 		Independence (again);
the ``Poisson Process";
Monty Hall! 		Due: Friday, April 11, 2003.

Downloadable Examples of Past Examinations in the Course
(Most With Solutions):

Final Exam and Solutions (F, '97) Second MT (W, '97) First MT and Solutions (W, '97)
Final Exam and Solutions (F, '99) Second MT and Solutions (F, '99) First Midterm (F, '99)
Final Exam and Solutions (W, '03) Second MT and Solutions (W, '03) First MT and Solutions (W, '03).
Final Exam and Solutions (F, '03). Second MT and Solutions (F, '03). First MT and Solutions (F, '03).

Optional further examples of problems from earlier chapters of the text,
as per student requests
(for preparation for final examination):

Ross, Chapter 4 Problems # 24, 27, 45, 49, 54, 62, 67. Be sure to understand basic ``modeling",
i.e., what ``kind of randomness"
a particular shape of probability
mass function models.
Ross, Chapter 5 Problems # 6, 8, 11, 14, 29, 34 39. Same comment as above;
also be sure how to describe
``events" involving RV's in
terms of regions of integration.
Ross, Chapter 6 Problems #12, 13, 25, 44, 51. Joint distributions:
know well ``events" as regions of integration;
sums of RV's and their expectations.
Ross, Chapter 7 Problems #24, 34, 41, 42, 47, 56. Properties of expectation and conditional expectation and variance.
Some of these problems in chapter 7 can be quite long.
Don't expect to do all of those suggested in a short period.
Look them over and try to analyze how to procede.
Then work out all the details on a couple of examples. Be sure to look at the ducks and the elevators (#55 and #56).

Announcement:
Final Exam 		Wednesday,
April 23, 2003,
Room B844, East Hall.
(Basement, Church Street end.) 		Note change of room! ``Can't wait!"