DEPARTMENT OF MATHEMATICS
UNIVERSITY OF TEXAS AT AUSTIN
M362K: Probability I
First-day Handout
Fall, 2011
Welcome to M362K. Here is some information and some ground rules. I will stick to the these rules, and
I assume you will, too. Read carefully and let me know if there is anything unclear. Treat this document as
a contract.
Course number: M362K Unique number: 55400 Class meets: TTH 9:30am-11:00pm Room: RLM 6.118
Instructor: Gordan Žitković Office Hours: T 11:00am-12:00noon, W 1:00pm-2:00pm Office: RLM 11.132
E-mail: gordanz [email protected] (there is an underscore between “gordanz” and “teaching”)
Course description: This course will cover the mathematical theory of probability, fundamental to further
work in probability and statistics, as well as many other fields in science, engineering, economics, etc. The
topics covered will include basic notions of probability, conditional probability and independence, various
discrete and continuous random variables, expectation and variance, joint probability distributions, the law
of large numbers, and the central limit theorem.
Formal Prerequisites: A grade of C - or higher in either M408D, M408L or M408S.
Prerequisites: Good knowledge of the material taught in M408D, M408L in M408S. In particular, you are
expected to be comfortable with set operations (union, intersection, complement, De Morgan rules, etc.),
geometric series, the series representation of the exponential function, the fundamental theorem of calculus,
computing integrals using a change of variable, and computing double integrals.
Textbook: J. Pitman Probability, ISBN 9780387979748
Course webpage: The online course-management system Blackboard will be NOT be used in this course. Instead, all the materials will be available in the teaching section of http://www.math.utexas.edu/~gordanz
Homework: A weekly (or so) homework will be assigned and its due date will be announced on the course
web-site. No late homework will be tolerated. It is extremely rude towards your graders/TAs. In return for
a strict adherence to this policy I will drop your lowest homework grade. You are allowed (and encouraged)
to discuss the homework problems with other students, but you have to write up the solutions yourself.
Homework assignments you turn in must be organized and stapled. Just like other business or official
documents, the homework assignments must be done carefully and written legibly on standard size paper.
Box answers where possible. Staple in the top left-hand corner. Write your Name, Course Number, Assignment Number, and Date on the first page. Put your last name on top of each page. Put solutions in order
and number pages.
The homework assignment will be due at the beginning of the class on the day it is due. Anything after
that will be considered late.
Exams: There will be two 75-min in-term exams (scheduled for Oct 18 and Nov 22), as well as a final exam
(scheduled by the university during the final exam period). If you miss the in-term for a documented reason
(illness, approved and previously announced religious holiday, or some other extraordinary circumstance),
your score on the final exam will be used in the grade calculations instead. In other words, your final exam
will be worth 65%. The two in-terms will focus on the material covered since the last exam but will require
knowledge of all the material covered so far. The final will be cumulative.
You are not permitted to use the textbook, your notes or any other written material during the in-terms
or the final exam. Calculators are also generally outlawed, unless I specifically state otherwise before the
exam. In return I will design the exams to be hands-on without being computationally overwhelming.
1
Grading: Here is how your final grade will be composed:
Final Exam
1st In-term
2nd In-term
Homework
40%
25%
25%
10%
and here is how the letter grade will be assigned (the second row refers to your final percentage score)
A
94 - 100
A90 - 94
B+
86 - 90
B
83 - 86
B80 - 83
C+
75 - 80
C
70 - 75
C65 - 70
D+
60 - 65
D
55 - 60
D50 - 55
F
0 - 50
There is no “curve” in this class. You are 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.
If you show up for both in-term exams and get an average score of at least 94%, you will be exempt from
the final exam and get an automatic A.
I need to stress the following point: the grade you get will be based only on the work you present in your
in-term and final exams and homework. I am not allowed to and I will not use any other information. In
particular, no extra credit work will be assigned.
Office hours and e-mail use: 1) Per university rules, I will not reply to/read e-mail sent to any address
other than the one above. 2) Please contact me via e-mail only for administrative reasons. If you have
questions about the material, please come to the office hours. 3) Please prepare before you come to the
office hours. Make sure you have read the appropriate sections from the textbook and that you are ready to
present your approach to the problem, as well as pinpoint the exact step at which you got stuck.
Religious holidays: 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.
Academic (dis)Honesty: 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 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
Students with Disabilities: The University of Texas at Austin provides upon request appropriate academic
accommodations for qualified students with disabilities. If you have a documented disability and you need
special treatment as a result of your disability, please let me know as soon as possible, but definitely within
the first 3 weeks of class. For more information, contact the Office of the Dean of Students at 471-6259,
471-4641 TTY.
The Q-drop date: The last day for a Q-drop is Nov 1.
2
Miscellaneous Advice:
1. 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 have been taught 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.
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.
2. 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).
3. 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.
Schedule of classes: (Section numbers refer to the textbook.)
#
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
Wday
TH
T
TH
T
TH
T
TH
T
TH
T
TH
T
TH
T
TH
T
TH
T
TH
T
TH
T
TH
T
TH
T
T
TH
Date
Aug 25
Aug 30
Sep 1
Sep 6
Sep 8
Sep 13
Sep 15
Sep 20
Sep 22
Sep 27
Sep 29
Oct 4
Oct 6
Oct 11
Oct 13
Oct 18
Oct 20
Oct 25
Oct 27
Nov 1
Nov 3
Nov 8
Nov 10
Nov 15
Nov 17
Nov 22
Nov 29
Dec 1
Material to be covered
Orientation. Section 1.1.
Section 1.1 (cont’d)
Sections 1.2 and 1.3
Section 1.3 (cont’d)
Section 1.3 (cont’d)
Section 1.4
Section 1.4 (cont’d)
Section 1.5
Section 1.5 (cont’d), 1.6
Section 2.1
Section 2.1 (cont’d)
Section 2.2
Section 2.2 (cont’d)
Section 2.4, 3.1 (Part I)
Section 4.5 (Part I), 3.1 (Part II)
Section 4.5 (Part II), Section 3.2
Section 3.3
Sections 3.4, 3.5
In-term I
Section 4.1
Sections 4.5 (Part III), 4.2 (Exponential dist’n)
Section 4.4
Sections 5.1 and 5.2
Sections 5.3 and 5.4
Sections 6.1, 6.2 and 6.3, 4.2 (Gamma dist’n)
In-term II
Sections 6.4 and 6.5
Moment Generating Functions. Simulations
3