Math 4810/5310 Probability
FALL 2014
Department of Mathematical and Statistical Sciences
University of Colorado Denver
Instructor: Burt Simon
Office: AB 4209
Office Hours: TR 3:00-4:00, or by appointment
Phone: 303 315 1710
Website: www.math.ucdenver.edu/~bsimon
Email: burt.simon@ucdenver.edu
Course dates/times: TR 12:30-1:45
Course location: NC 1314
Text: Fundamentals of Probability
with Stochastic Processes, 3rd ed.
by Saeed Ghahramani
Welcome! Probability is a fascinating and very useful mathematical theory. Math
4810/5310 is a standard introduction to probability theory. By successfully completing
this course you will be ready to take courses in mathematical statistics, probabilistic
modeling, stochastic processes, financial engineering, actuarial science, and various
engineering fields. Please check the class web page regularly, which can be linked to from
my page at math.ucdenver.edu/~bsimon. The class web page will have the weekly
assignments, announcements, exam solutions, etc. I encourage students to participate in
class by asking questions and answering (rhetorical) questions that I ask during class.
University Course Catalog Description:
Examines elementary theory of probability, including independence, conditional probability, and
Bayes’ theorem; random variables, expectations and probability distributions; joint and conditional
distributions; functions of random variables; limit theorems, including the central limit theorem. Note:
No co-credit with MATH 3800. Prereq: MATH 3191; Coreq: MATH 2421. Cross-listed with MATH
5310. Semester Hours: 3 to 3
Course Overview: Introductory probability courses like this one cover axioms of
probability, combinatorial probability, conditional probability, random variables (discrete,
continuous, and multivariate), Expected value (mean, moments, variance, covariance, etc.),
and some limit theorems (laws of large numbers, Central Limit Theorem).
Course Goals and Learning Objectives:
A. Overall Learning Objectives: By successfully completing this course, students will
be familiar with all the basic concepts of probability theory listed in the Course
Overview, and will understand how they tie together. Students will be able to
calculate probabilities, expected values, etc., and be able to formulate probabilistic
solutions for simple applied problems.
B. Learning Outcomes:
 Problem Solving: Students will learn to solve problems involving uncertainty
that are posed as generic probability calculations, and as real-world
applications of probability theory.
 Creative Thinking: Students will learn to distill a probability problem from a
description where it may not be obvious how probability theory applies
 Critical Thinking: It is easy to misapply probability theory, so students will
learn to apply the theory correctly.
C. Major Topics: axioms of probability, combinatorial probability, conditional
probability, random variables (discrete, continuous, and multivariate), Expected
value (mean, moments, variance, covariance, etc.), and some limit theorems (laws of
large numbers, Central Limit Theorem).
D. Rationale: Probability is required as a prerequisite for many upper division math
courses, like statistics, probabilistic modeling, stochastic processes; and is useful in
business, engineering, and other technical fields.
Course Prerequisites: Math 3191 (linear algebra)
Course Credits: 3 credit hours
Required Texts and Materials: Fundamentals of Probability with Stochastic Processes,
third edition, by Saeed Ghahramani
Course Schedule:
The following schedule of course materials covered is tentative, but the dates of the exams
will not change.
DATES (class times)
TOPICS
SECTIONS FROM TEXT
August 18,20
August 25,27
September 3
September 8,10
September 15,17
September 22,24
Sept. 29, Oct. 1
October 6,8
October 13,15
October 20,22
October 27,29
November 3,5
November 10,12
November 17,19
November 24-30
December 1,3
December 8,10
Axioms of probability
Combinatorial methods
Conditional probability
Discrete random variables
Discrete random variables
Review and Exam #1
Continuous random variables
Continuous random variables
Multi-variate distributions
Multi-variate distributions
Review and Exam #2
E(X), Var(X), Cov(X,Y), Cor(X,Y)
Conditioning on random variables
Sums of r.v.'s and limit theorems
Thanksgiving Break
Catch-up and Review
Final exam (date to be announced)
sections 1.1 - 1.7
sections 2.1 - 2.4
sections 3.1 - 3.5
sections 4.1 - 4.5
sections 5.1 - 5.3
sections 6.1 - 6.3
sections 7.1-7.5
sections 8.1 - 8.3 and 9.1
sections 9.1 - 9.3
sections 10.1 - 10.3
sections 10.4 - 10.5
sections 11.1 - 11.5
Assignments: I will assign homework problems from the textbook (approximately)
weekly. Typically the assignment will be posted on the class web page on Tuesday, and will
be due the following Tuesday. You are expected to turn in every homework assignment on
time, since the purpose of the homework each week is to practice the material covered in
class that week. Furthermore, homework sets will be discussed in class the day they are
due, so late assignments will not receive full credit. Homework sets are expected to be
written up neatly so they are easy to read (preferably using Word or Latex).
Working collectively on the homework assignments is encouraged! There is no penalty, but
please list the people you worked with on the papers you turn in.
Basis for Final Grade: Your final grade will be based on your exam scores (two midterm
exams and a final exam), weekly homework sets, and intangibles such as class
participation. The intangibles can only increase your grade.
Exam and homework grades will start out as numerical (e.g., between 0% and 100%), but
will be “curved” and translated into letter grades, “A+” at the top and “F” at the bottom.
These letter grades are associated with the same numerical values that your GPA is based
on, i.e., A+ = 4.3, A = 4.0, A- = 3.7, B+ = 3.3, B = 3.0, B- = 2.7, C+ = 2.3, C = 2.0, C- = 1.7,
D+ = 1.3, D = 1.0, D- = 0.7, and F = 0.0.
In the absence of “intangibles”, your final grade will be a weighted average of the letter
grades on your exams and homeworks. You will get a simple homework grade, which will
be the average of the individual scores, with the lowest score deleted. The weightings will
be as follows: Homework (20%), Midterm Exam #1 (25%), Midterm Exam #2 (25%),
Final Exam (30%).
Grade Dissemination: I will try to grade homework sets within a week of when they are
due, and exams by the next class after they are taken. They will be returned in class with
grades on them. If you sense a mistake in my grading, please send me an email, or come to
my office hours to discuss.
Course Policies
A. Attendance: I will not take attendance, but students are expected to attend every
class. You will be responsible for material I cover in class, whether or not it is in the
textbook. Class participation is one of the important “intangibles” that can impact
your grade.
B. Late Work Policy: Normally I will not accept late homework sets, and I will not make
arrangements if you miss an exam. Under unusual circumstances arrangements can
be made. Try to give me as much lead time as possible if you know something will
force you to be late with an assignment, or miss an exam.
C. Extra Credit Policy: There is no “extra credit” in general, but students can try to raise
their grades by being attentive (and participating constructively) in class, and
demonstrating competence in my office hours.
D. Grades of “Incomplete”: I will follow university procedures on “incompletes”, i.e.,
they are only given in situations where unexpected emergencies prevent students
from completing the course and the remaining work can be easily finished the
following semester. Incomplete work must be finished the next semester or the
grade automatically turns into an F.
E. Group Work Policy: Students are encouraged to collaborate on homework sets, as
long as they acknowledge their collaborators. There is no penalty for working
together. Of course, no collaboration is allowed on exams, as that is considered
cheating.
F. Announcements: I will use the class web page for all communication that is meant
for the whole class. Please check the page regularly. Private communication is best
done by email. I will typically respond within a day.
G. Laptops, Cell Phones, etc.: You are free to use your devices as you see fit during
class. (No phone calls or texting, of course.) The rules during exams will be
announced prior to the tests. Usually my exams are open-book, open-notes, but
electronic devices (calculators, computers, etc.) are not allowed.
H. Civility: Students are expected to be quiet and attentive during class, although
raising your hand to ask a question or make a comment is welcome and encouraged.
 Dishonesty: Students are expected to understand intuitively what proper ethical
conduct means in the context of a college mathematics course. If you are caught
cheating you could fail the class or (at least) have your grade lowered, so don’t
even try it.
Fall 2014 CLAS Academic Procedures and Deadlines
The following policies, procedures and deadlines pertain to all degree-seeking students in the
College of Liberal Arts and Sciences (CLAS). Please also consult the Official University
Academic Calendar and see you advisor if you have questions or concerns.
 Schedule verification: It is each student’s responsibility to verify online that his/her
official registration and schedule of classes is correct before classes begin and prior to the
drop/add deadline. Failure to verify schedule accuracy is not sufficient reason to justify a
late adds or drops.
 E-mail: Students must activate and regularly check their official CU Denver e-mail
account for university related messages. Those who forward email should check CU
Denver e-mail regularly for messages not automatically forwarded.
 Waitlists:
 Students are automatically notified if they are enrolled in a class from a waitlist via
their official CU Denver email account.
 Students are not automatically dropped from a class if they never attended, stopped
attending, or do not make tuition payments, though instructors may request
administrative drops.
 Waitlists are purged after the 1st week of classes. To add a course from August 26September 3, it is the student's responsibility to get a CLAS Instructor Permission to
Enroll in a Course form at http://www.ucdenver.edu/academics/colleges/CLAS/clas-
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advising/Pages/CLASAdvising.aspx or
http://www.ucdenver.edu/academics/colleges/Graduate-School/Pages/default.aspx,
have it signed electronically or in person and submit it according to the instructions on
the form. Students and faculty will receive emails with directions for completing
registration via official university email and students must complete registration and
verify their schedules before census, September 3rd, by 5p.m. After Sept 3: students
should meet with their CLAS advisor to learn more about how to petition to add a
course late.
Late adds (after September 3, 2014) will be approved only when circumstances
surrounding the late add are beyond the student’s control. This will require a written
petition and verifiable documentation. Petition forms are available in the CLAS advising
office, NC 4002, or the Graduate School, LSC 1251. The signature of a faculty member on
a Schedule Adjustment Form does not guarantee that a late add petition will be approved.
Late drops (after November 10, 2014) will be approved only when circumstances
surrounding the late drop are beyond the student’s control. This will require a written
petition and verifiable documentation. Petition forms are available in the CLAS advising
office NC 4002 or the graduate school, LSC 1251. The signature of a faculty member on a
Schedule Adjustment Form does not guarantee that a late drop petition will be approved.
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Tuition: Students are responsible for completing arrangements with financial aid, family,
scholarships, etc. (depending on tuition plan selected) to pay their tuition prior to Census
Date, September 3, 2014. Students who drop after that date are (1) financially responsible
for tuition and fees, (2) academically responsible and will receive a "W" grade, and (3) are
ineligible for a refund of COF hours or tuition.
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Graduation:
 Undergraduate students wishing to graduate in Fall 2014 should (1) first meet with
their CLAS advisor; (2) meet with their major and minor advisor(s), who will
complete the electronic form required to verify eligibility to graduate; and (3) apply
for graduation online through UCDAccess. These steps must be completed by no later
than 5PM on September 3rd, which is an absolute deadline without exception.
 Graduate students wishing to graduate in Fall 2014 must apply for graduation online
through UCDAccess and have a Request for Admissions to Candidacy on file with the
CU Denver Graduate School (LSC 1251) no later than 5 PM, September 3, 2014,
which is an absolute deadline without exception.
Important Dates and Deadlines
All dates and deadlines are in Mountain Standard Time (MST).
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August 18, 2014: First day of classes.
August 24, 2014: Last day to add or waitlist a class using the UCDAccess student portal.
Last day to drop a class without a $100 drop charge--this includes section changes.
September 1, 2014: Labor Day--no classes, campus closed.
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September 3, 2014: Census date.
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9/3/14, 5 PM: Last day to add structured courses without a written petition for a late
add. This is an absolute deadline and is treated as such. This deadline does not apply
to independent studies, internships, project hours, thesis hours, dissertation hours, and
late-starting modular courses.
 9/3/14, 5 PM: Last day to drop a Fall 2014 course or completely withdraw from all
courses using a UCD Access Portal and still receive a tuition refund, minus the drop
fee(s). After this date, tuition is forfeited and a "W" will appear on the transcript. This
includes section changes. This is an absolute deadline.
 9/3/14, 5 PM: Last day to apply for Fall 2014 graduation.
 9/3/14, 5 PM: Last day to request pass/fail or non-credit option for a course.
 9/3/14, 5 PM: Last day to petition for a reduction in Ph.D. dissertation hours.
September 15-24, 5 PM: Early Alert open to faculty
October 27, 2014, 5 PM: Last day for non-CLAS majors to drop individual courses
instructor permission only. After this date, a dean’s signature is required on a Schedule
Adjustment Form. Note: Withdrawal from all classes does not require individual
instructor signatures. Students must obtain a dean’s signature to withdraw from all
classes.
November 10, 2014, 5 PM: Last day for CLAS majors to drop individual courses or
withdraw from all classes without a petition and dean’s approval. After this date, a petition
is required in order to obtain dean’s signature approval on a Schedule Adjustment Form.
Petition forms are available in NC 4002 for undergraduates and LSC 1251 for graduates.
November 24-30: Fall break, no classes but campus open.
November 27: Thanksgiving Day--no classes, campus closed
December 6, 2014: Last day of classes
December 8-13: Final Exam week
December 13: Fall 2014 commencement
December 22, 2014: Final grades available on UCDAccess and transcripts (tentative).