M362K(56325)
Probability I
Spring 2011
University of Texas at Austin
Instructor: Milica Čudina
First-Day Information Sheet Technicalities
Lectures: Tue and Thu 2:00-3:30pm
Location: ENS 116
Office Hours: Tue/Wed/Thu 11:00-11:45am
Office: RLM 13.142
My e-mail: [email protected]
Phone numbers:
(512)232-6186 (the instructor’s office)
(512)471-7711 (Department of Mathematics - main office)
(512)471-9038 (Department of Mathematics - main office(fax))
REQUIRED text: “Probability” by Jim Pitman
URL: http://www.math.utexas.edu/users/mcudina/
About the Course
A few (serious) introductory remarks
Course description. This course is intended to introduce the student to the basics
of probability theory. It is supposed to build a formal framework for the notions we
encounter in everyday life (e.g., frequency, probability, randomness, distribution, expectation) and then expand them to encompass the more abstract objects (e.g., random
variables, distribution and density functions, correlation, independence, conditioning).
The establishment and study of the mathematical formalism of probability theory will
enable the class to construct a common ground for the many models of stochastic phenomena that are considered in a great number of varied applications (e.g., in natural and
social sciences, economics, engineering). Along the way, many examples will be explored
to serve as both the inspiration and the background for the more “theoretical” topics.
The course will occasionally involve simulations (generating “random” quantities using
computer software) to give a vivid demonstration of the necessity for the underlying
theory and the behavior of some of the most common models for random values (i.e.,
probability distributions). At opportune moments during the term, we intend to cover
a few simple limit theorems which are essential for both the statistical studies and to
make certain more complicated probabilistic models simpler and more tractable.
In short, the most important goals of this course are
– to increase the students’ literacy when it comes to subjects involving probabilistic notions;
– to establish the basics of probability theory needed to proceed to more involved courses
later on in the curriculum;
– to enable the students to conduct and interpret some simple simulations;
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– to expose the student to many examples;
– to gain intuition for solving problems involving random phenomena . . .
Prerequisites. Grade of at least C in M408D.
A few words about the assignments and grading
You will be having six homework assignments (due on the dates indicated in the table at the
end of this document, and always in the beginning of class). There will also be two in-term
exams during the session, and a final exam.
Homework. This is important information: I will not accept homework that
does not conform to the guidelines that follow! Homework assignments you turn
in must be organized and stapled. As will business or official documents, the homework
assignments must be done carefully and written legibly on standard size paper according to
the following instructions. Please do homework on standard size good quality paper. Please
write only on the front of each sheet. Box numerical answers where possible. Staple in the
top left-hand corner. On the first page and the outside page write your Name, Course
Number, Assignment number, and Date. Also, put your last name on each page. Put
solutions in order and number the pages.
The lowest homework score will be dropped.
In-Term Exams. These exams will be administered during regular lecture time and will
take place in the same classroom. Each exam will focus mostly on the material covered since
the previous exam, but it is quite possible that some of the problems will refer to earlier
material. Anybody whose average score in both in-term exams is above 90 will get an
automatic A and will not be required to take the final exam. To clarify the last point: If
you want to be exempt from the final exam, you must take both in-term exams, and their
average score must be above 90%.
To prepare for the exams, you will be given past exams and assigned problems from the
textbook. These are meant to introduce you to the format of the actual exam and the
material covered therein - not the exact content of the real exam.
The Final Exam. The final exam is going to be comprehensive. That means that any
material covered in class or assigned as reading can (and probably will) appear on the final.
The registrar’s office “hopes to publish the exam schedule by April 4.”
These are the things you must not to bring to the exams:
i. books, notes, manuals, anything containing solved problems;
ii. your own tables of the standard normal distribution (you will get a new copy to use
during the exam, if needed).
These are the things you should to bring to the exams:
i. paper to work out your solutions on;
ii. any type of calculator.
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Your scores in all of these will be incorporated into your final grade according to the following
scheme:
Homework assignments (total): 5%
In-term exams (total): 50%
Final: 45%
Solutions to homework assignments and midterm exams will be presented in class.
In the end, let me caution you that:
– no late homework will be accepted and
– there will be no make-up exams. If you provide me with a written proof that you
absence was “legitimate”(e.g., a note from your doctor or your lawyer). In that case
you can expect one and only one in-term exam you missed to be dropped from the
calculation of your final score and your score from the final exam will be substituted for
the score from the exam you missed.
No plus/minus grades will be awarded in this course. The final letter grades will be assigned
relative to your numerical score obtained from the above scheme in the following way
A : 90 − 100
B
: 80 − 90
C
: 65 − 80
D
: 55 − 65
I do not “curve” the grades!!!!!
A few bits of friendly advice
Take your homework assignments seriously - This course starts with the material that
does not appear to be very sophisticated mathematically, but the computations will get
very elaborate very soon. In particular, the skills you should have acquired in calculus
and earlier will be essential. More importantly, the topics covered and the manner in
which this is done may strike most of the student as unexpected - most of you have never
taken a class in which an axiomatic system is built from scratch. This means you will
have to actively attempt to immerse yourselves in the subject. The only way to deal
with all this is for you to work individually and continuously.
Discuss the course with your colleagues - This advice is closely connected to the one
above. In order to be able to participate in class, you first need to build up a vocabulary
- and there will be a lot of new vocabulary in the beginning. Who better to practice the
new concepts with than your classmates who are in the same situation? I suggest that
you try to work on homework assignments in pairs and small groups. Of course, you
will be required to write-up your own final version (and I urge you to do so - that is the
only way you will be able to tell what your individual knowledge is, as opposed to the
collective knowledge of your study-group).
Don’t try to cheat - This is an unpleasant topic, but unfortunately a necessary one! One
is often tempted to stretch the boundaries of mere discussion/collaboration with a fellow
student into the territory of pure and simple cheating. In short, everything that you
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present as your own work (especially the work that is supposed to be graded!) should,
in fact, be your own work, and not something copied from an external source. In case
that a student is caught in violation of the principles of academic honesty enforced at
this university, he/she is immediately reported to the higher authorities and assigned a
failing grade in this course. You are expected to have read and understood the current
issue of General Information Catalog, published by the Registrars Office, for information
about procedures and about what constitutes scholastic dishonesty. Also please visit
http://deanofstudents.utexas.edu/sjs/academicintegrity.html.
Get familiar with the required text - This is advice that everybody gives, but nobody
takes - but do try to take a peak into the material we are going to cover in advance. It
will make your journey less stressful, and will save you time and energy in the long run.
You are fortunate in that the required text contains tons of examples and problems. We
will not have the time to cover all of them in class, but that does not mean you should
not work on them by yourselves. In fact, self-study should be understood as an integral
part of this course.
Have realistic impressions of your performance - The grading scheme for this course is
described above and I do not intend to stray from it. You are solely responsible for
keeping a tally of your scores throughout the semester and entering your results in the
grading formula above to avoid any surprises at the end of the semester.
UT mandated notes
“The University of Austin provides upon request appropriate academic
accommodations for qualified students with disabilities. For more information, contact
the Office of the Dean of Students at 471- 6259, 471-6441 TTY.”
“Religious holy days sometimes conflict with class and examination schedules. Sections
51.911 and 51.925 of the Texas Education Code relate to absences by students and
instructors for observance of religious holy days.
Section 51.911 states that a student who misses an examination, work assignment, or
other project due to the observance of a religious holy day must be given an
opportunity to complete the work missed within a reasonable time after the absence,
provided that he or she has properly notified each instructor.
It is the policy of The University of Texas at Austin that the student must notify each
instructor at least fourteen days prior to the classes scheduled on dates he or she will
be absent to observe a religious holy day. For religious holidays that fall within the
first two weeks of the semester, the notice should be given on the first day of the
semester. The student may not be penalized for these excused absences but the
instructor may appropriately respond if the student fails to complete satisfactorily the
missed assignment or examination within a reasonable time after the excused absence.”
On email and office hours - Email should be used for brief messages about the organization of and current goings on in the course. As a rule, you should first consult the
first-day handout to see if your question is answered here. If there is still any ambiguity,
contact the instructor. Know that your instructor is handling a great number of email
messages. You should not expect to have your particular email answered in less than
48 hours. You should not be asking mathematical questions via email, since they are
incredibly difficult to answer through a typed message. To get an answer to this type
of questions, you should come to office hours and ask in person. When coming to office
hours, you should be able to present the mathematical question you have, the route(s)
you took in attempting to solve the problem and the obstacles you encountered.
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A tentative schedule
WEEK 1
WEEK 2
WEEK 3
WEEK 4
WEEK 5
WEEK 6
WEEK 7
WEEK 8
WEEK 9
WEEK 10
WEEK 11
WEEK 12
WEEK 13
WEEK 14
WEEK 15
Jan, 18th
Jan, 20th
Jan, 25th
Jan, 27th
Feb, 1st
Feb, 3rd
Feb, 8th
Feb, 10th
Feb, 15th
Feb, 17th
Feb, 22nd
Feb, 24th
Mar, 1st
Mar, 3rd
Mar, 8th
Mar, 10th
Mar, 22nd
Mar, 24th
Mar, 29th
Mar, 31st
Apr, 5th
Apr, 7th
Apr, 12th
Apr, 14th
Apr, 19th
Apr, 21st
Apr, 26th
Apr, 28th
May, 3rd
May, 5th
Orientation. Reading Assignments. Section 1.1
Sections 1.1 (cont’d). Section 1.2.
Section 1.2 (cont’d). Section 1.3
HW1 Overview. Section 1.3 (cont’d)
Section 1.3(cont’d)
Problem solving session.
HW2 Overview. Section 1.3 (cont’d). Section 1.4
Problem solving session.
Section 1.4 (cont’d).
HW3 Overview. Section 1.4 (cont’d). Section 1.5
Section 1.5 (cont’d). Section 1.6
Section 2.1
HW4 Overview. Sections 2.2, 2.4
Sections 3.1, 4.5
Section 3.2
In-term I
In-Term I Overview. Section 3.3
Section 3.3 (cont’d)
Sections 3.3 (cont’d), 3.4, 3.5
Sections 4.1, 4.2
HW5 Overview, Section 4.2 (cont’d)
Section 4.2 (cont’d)
Sections 4.2 (cont’d), 4.4
Sections 5.1, 5.2
Section 5.2(cont’d), Section 5.3
Section 5.3(cont’d),5.4 (part)
Sections 6.1, 6.2, 6.3
HW6 Overview, Sections 6.4, 6.5
In-Term II
Moment generating functions
HW1 Out
HW1 Due
HW2 Out
HW2 Due
HW3 Out
HW3 Due
HW4 Out
HW4 Due
HW5 Out
HW5 Due
HW6 Out
HW6 Due
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