Probability Theory and Applications
MATP 4600/DSES 4750

Syllabus
Instructor: Dr. Peter R. Kramer
Office: 310 Amos Eaton
Hall
Telephone: (518)
276-6896
Email: kramep@rpi.edu
Class Meetings: Mondays and
Thursdays, 2:00-3:50PM in Amos Eaton 215
Office Hours: Wednesdays 2-3 PM and
Fridays 4-5 PM
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Resources
Course
Objectives
Exams/Grading
Learning
Strategy
Honesty
Schedule
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Resources
- Probability and Statistics, Morris H. DeGroot and Mark J.
Schervish, Third Edition, Addison Wesley, 2002. A serious and
comprehensive textbook on probability and statistics, oriented toward an
engineering mindset. If you are unsure about which textbook to choose for
this course, I would recommend this one. Moreover, this book should also
serve you well for the Mathematical Statistics class in the spring.
- Introduction to Probability, Dimitri P.
Bertsekas and John N. Tsitsiklis, Athena Scientific, 2002. A lively
"lecture note" presentation of the subject of probability that should
appeal to strong students interested in mathematics and physics. The book
focuses more on interesting aspects and ways of thinking about
probability rather than following a standard, detailed textbook
approach.
- Introduction to Probability and Mathematical
Statistics, Lee J. Bain and Max Engelhardt, Second Edition,
Duxbury,1992. This was the text used for the probability and statistics
classes last year. It has a more concise conceptual treatment than
deGroot & Schervish, but many more simple examples. However, I have
not heard good reviews from students about this book.
- Probability for Risk Management, Matthew J.
Hassett and Donald Stewart, ACTEX Publications, 1999. A development of
probability oriented toward actuaries which also serves as a relatively
easy introduction for those who may find deGroot and Schervish too
demanding.
- WebCT (Blackboard Learning System) will be used
for some aspects of course management. You can get started by going to
http://rpilms.rpi.edu and
consulting the document describing the use of WebCT/Blackboard in this
class.
- Maple may be used for some parts of the course. By my
understanding, this is accessible to all Rensselaer students. If you
would like to learn more about Maple, you may find the department's Maple
Resources page of use.
Course Objectives
- To learn and use various mathematical techniques which are generally
useful in probabilistic analysis and reasoning
- To gain experience with setting up, analyzing, and interpreting the
results of probabilistic models in applied settings in science and
industry
Exams/Grading
Your course grade will be weighted as follows:
- Homework: 25%
- Midterm #1: 20%
- Midterm #2: 25%
- Final exam: 30%
Your course grade can be enhanced by active and substantive contribution
to discussions in class and on the WebCT site. You can be awarded as much
as 5 percentage points on your final grade for exceptionally insightful and
thoughtful input and questions
Late homework will be penalized 10 points (out of 100) per working day.
Once I post solutions to the homework (which could be as soon as the class
after the assignment was due), no more homeworks will be accepted for
credit. If you have need for an extension on your homework, you should ask
me in advance of the due date. Homework is due at 2 PM on the
due date specified on the calendar; submissions later in the class or day
will be penalized 5 points.
Takehome components of exams are due at 2 PM on the due date
specified on the calendar. I will accept submissions until 4 PM with
a 10 point penalty, but nothing later than that without an excellent
excuse.
The grading scale for undergraduates is:
- A: 90% +
- B: 80-89%
- C: 70-79%
- D: 50-69%
- F: 0-50%
Graduate students are graded in the same way for scores of 70% and above,
but they will receive a grade of F for scores between 0-69%.
If you miss an exam, you will only be permitted to make up the exam if you
obtain an explanatory note from the Dean of Students indicating that you had
a valid excuse (such as serious illness). In any event, you must contact me
within 24 hours of a missed exam with at least a preliminary explanation if
you wish to make it up. Unexcused absences (including "forgetting" about the
exam) will result in a 0 score for that exam.
Your grade is based solely on performance, not effort. There is no official
"mercy" clause for a bad exam. However, I do sometimes adjust the final
grade in your favor if your work demonstrates a strong upward trend or a
generally consistent performance at a certain grade level with the exception
of a rare disaster. Such grade adjustments are given purely at my
discretion, and are not motivated by external matters such as your need to
maintain a certain GPA for financial aid, domestic tranquility, etc. I view
grades simply as a means of reporting, as accurately as possible, the
demonstrated level of your mastery with the material.
- You may only appeal scores on exams based on factual criteria (a
correct answer was marked wrong, or scores were added incorrectly). Any
such legitimate appeals will only be accepted within one week of the date
on which the graded exam was returned to the class. I will not entertain
quibbles about how many points of partial credit you think you should have
been given on some problem. Students making frivolous appeals will be
given one warning, after which further nuisance appeals will be penalized
by as many points as the student was frivolously arguing.
Back to top
I will direct the class
according to the following learning strategy:
- Students preview the sections of their textbook pertaining to the
material to be covered in class before
the class. It is not necessary to have a thorough understanding
of the section after a first reading, but knowing the basic facts and
content should help in following the class discussion. In particular,
I do not plan on spending much time in class on simply stating facts
and definitions which students can more easily read in a nicely typeset
textbook (as opposed to my childlike scrawls). Rather, I will assume
students have at least looked over the section enough to have
encountered new definitions and classifications, so that I can spend
the class time explaining more about the "how" and "why" of the
material rather than the "what."
- Students attend class as much as possible, and obtain class notes
from a friend when they are unable to attend. The material covered in
class is intended to supplement, and not simply restate, the material
in the textbook. Moreover, the class discussion will emphasize those
aspects of the material which I find most important (and are therefore
most likely to appear on the exams).
- Students work either alone or with a small group of colleagues to
solve the homework problems. A pair of students may submit a single set
of homework solutions with both students receiving the same grade for
that assignment. While collaboration is encouraged to stimulate
learning and understanding, each student is responsible for
understanding any solution submitted under his or her name. If the
assigned homework problems are too difficult, students should work out
some of the simpler problems from the related sections of their
textbooks until they have gained enough confidence and skill to tackle
the assigned problems. Students may in particular want to work on those
problems for which answers appear in the back of the book so they can
check their work and understanding. If students do not feel
sufficiently confident with the material through self-study or
consultation with colleagues, they should seek further assistance from
the professor during his office hours.
- Students review for exams by checking that they are familiar with the
material from the classes and textbook sections to be covered, can
still do the homework problems from the relevant sections, and by
taking one or more practice exams until they are satisfied with their
performance.
Honesty
- Evaluating student performance is an important part of the service
provided by Rensselaer, and for it to be meaningful, it must be based
on fair and honest representations. Acts which violate this trust
undermine the educational process.
- The general rules governing academic honesty in this course are
those found in the Rensselaer Handbook of Student Rights and
Responsibilities, with the following clarifications:
- Unless otherwise indicated, you may cooperate in small groups in and
outside of class on the solution of homework problems. You are
strongly encouraged to work with a partner on homework, and may turn in
one solution set per pair. While you may work together in groups
larger than 2, each homework submitted should be written essentially
independently once the ideas are hashed out. Generally speaking, you
should show your work and explain your calculations clearly and
coherently to achieve most of the credit.. It is not permissible for
one pair to simply copy the solutions of another pair, even if they are
working together. If there is evidence for such copying, all people
involved will be penalized 10 points for the first such infraction, 20
points for the second, 30 points for the third, and so on in arithmetic
progression. Please believe that I am able to detect trivial attempts
to conceal a copying operation. The worst penalty for not making your
own independent and serious effort on the homework is, of course, a
disappointing performance on the exams. Don't let your partner or your
friends do your thinking for you!
- You may under no circumstance collaborate on examinations or
misrepresent another person's work as your own on examinations.
- You may not bring books, notes, or electronic instruments to
examinations, except for one single
(8.5 by 11 inch) sheet of notes in your own handwriting.
- Students who violate the spirit or letter of these rules are
subject to penalties according to the principles outlined in the
Rensselaer Handbook, in addition to receiving a zero on any work on
which cheating has taken place. In addition, I will report all
instances of academic dishonesty to the Dean of Students.
Schedule
- The dates for topical coverage are approximate. The exam dates are
tentative for the moment, but will be fixed in the first week or two.
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Dates
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Topics
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August 28
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Conceptual Foundations of Probability
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August 31--September 11
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Counting and Combinatorial Techniques
No class on September 4
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September 14
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Conditional Probability, Independent Events, and Bayes' Rule
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September 18--21
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Discrete Random Variable Theory
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September 25--28
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Binomial Distribution Model and Generating Functions
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October 2
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Other Discrete Probability Model Examples
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October 5
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Exam 1 in class
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October 10--19
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Continuous Random Variable Theory
Monday,
October 9 class moved to Tuesday, October 10
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October 23-26
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Continuous Probability Model Examples
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October 30--November 2
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Joint Probability Distributions
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November 6--16
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Characterizations of Relations between Random Variables
Exam 2, Monday, November 13 in
class
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November 20--30
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Functional Relationships between Random Variables
No
class November 23
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December 4--7
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Probability Limit Theorems
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| December 14 |
Final exam, 6:30-9:30
PM |
Date Last Revised: 09/06/06