Download Probability Theory

Probability Theory
MA 381/581
Course Information
Fall 2008
Instructor
Abbas Alhakim, Ph.D.
361B Science Center
Tel. 268-3831
http://people.clarkson.edu/~aalhakim
[email protected]
Office Hours: 1:00PM--2:30 PM MTW, 12 PM --1 PM on Tuesday, or by appointment.
Lectures
Monday, Wednesday and Friday
4:00--4:50am
SC 362
Textbook:Probability and Statistics (third edition) by DeGroot and
Schervish
Course Content and Learning Objectives:
Catalogue description: Sample spaces; combinatorial analysis, the concept of
probability; random variables, expected values; and distributions including
hypergeometric, binomial, Poisson, and normal.
Details: This course deals with the concepts of probability theory. Starting with the
basic axioms that define the subject, we will cover such techniques of calculating
probabilities ranging from counting methods to integration, also discussing the meaning
and interpretation of the probability of a random outcome. Important concepts include
conditional probability, independence of events; random variables: their densities,
distributions, distributions of their transformations, their measures of centrality and scale
through the study of medians, mathematical expectations, moments, variances and
moment generating functions. In particular, we will discuss a collection of random
variables that are most widely used in applications (binomial, geometric,
hypergeometric, exponential, normal distributions and more). We will also study-mathematically--the law of large numbers (the law of averages) and the Central Limit
Theorem. Throughout the course of this discussion examples that relate these theoretical
concepts to the world of applications will be provided.
Also some [hopefully] entertaining classical problems that shed light on the motivation
and objectives of the subject matter will be seen. Detailed objectives of individual
lectures will be given in the beginnings of the lecture notes.
Graduate students: the content is basically the same, but you are expected to do more
work and you will be assigned a few more problems (problems listed with superscript G).
Prerequisites and Course Outcomes:
Students who intend to take this course should be aware that the content is inherently
mathematical. (in fact much more so than Stat 383). The main vehicle for understanding
the material is a solid understanding of Calculus: differentiation, integration, infinite
series as well as Calculus of two or more variables. Note that some of the essential
Calculus concepts will be briefly recalled as needed, however, Calculus I, II and III are
all necessary prerequisites.
The global objective of the course is to familiarize the students with the concepts of
randomness, equip them with the methodology needed to deal with randomness and
uncertainty, as encountered in Economics, Engineering or scientific disciplines. This
will be accomplished mainly by the examples that illustrate the general theory and by
the problems that will be assigned.
Academic Integrity: "The Clarkson student will not present, as his or her own, the
work of another, or any work that has not been honestly performed, will not take any
examination by improper means, and will not aid and abet another in any dishonesty."
(Clarkson Regulations)
Any student violating this standard will receive an F in the course and will not be
allowed to submit any further work.
You are allowed, and in fact expected, to work with other students on homework and
projects. However, what you turn in for grade must represent your own understanding of
the assignment in your own writing style.
Exams: There will be three midterm exams in addition to the final. The tentative dates
are:
Test 1: Friday, October 3th
Test 2: Monday, October 27th
Test 3: Monday, November 24th
Final:
Week of December 8
Tests will be given in class during the regular class time. The material to be covered on
exams will be outlined at least two classes before the exam. The Final Exam will be
comprehensive, covering the whole course. Anyone unable to take an exam should
contact me ahead of time and submit a valid excuse in order to be given a make up
exam. Any exam missed without prior approval receives a grade of zero. Any appeals to
grades should be done in the instructor’s office rather than the classroom.
Grading
Attendance/class participation/attitude/willingness to learn new things ……………5%
Homework……………………………………………………....................................10%
Projects…………………………………………………….........................................10%
Quizzes………………………………………………………………………………...8%
The three midterm Tests(combined)............................................................................42%
Final Exam……………………………………………...............................................25%
Letter grades will only be given at the end of the term using the weight described above
and following the rule:
B: 80—84.99%
B+: 85—89.99%
A: 90 — 100%
C: 70—74.99%
D: 60—64.99%
C+: 75—79.99%
D+: 65—69.99%
Below 60%: F
Homework
Suggested homework sets from all the sections that will be covered are listed below.
Exercise numbers with a superscript (*) are particularly important and some (or all) of
them will be collected for grading as will be announced in due time. Exercises with a
superscript (G) are ONLY required for graduate students while every one is encouraged
to try them. No late homework will be accepted (unless prior arrangement is made).
Quizzes will be given on (some) Fridays and will be announced earlier in the week.
There will be no make up quizzes.
Projects
About three projects will be given during the semester which will typically involve
extensive computation/simulation. Every two students must team up to do and submit
one project report, (Grad students have to work individually.) The project must be well
written with all steps/ideas expressed clearly. The project report must be typed.
Homework Sets:
1.4: 1,2*,3,5G,6*,7,8*
1.5: 4, 5, 6*, 7, 8*, 9*, 10,
11*, 12G,13G
1.6: 2*, 4*, 6*, 8*
1.7: 4, 5, 6*, 7, 8*, 9, 10*
1.8: 6, 9, 10*, 12*, 15,
16*, 17, 18, 19
4.1: 3,4*,5,6*,7G,8*,11*
4.2: 2,3*,4*,7*,9*
4.3: 2, 4*,5,6*,8G,9*
4.4: 1,2*,6*,7,12*,13G
4.5: 2*,6a*, 6bG
4.6: 2*,3*,6*,7,9*
4.8: 1,2*,3*,4G,5,6*
1.9: 1, 2*, 3, 4*, 8*,
11G
1.10: 1, 2, 3, 5, 6*,
8*,10*
2.1: 2, 4*,5*,6*,9, 10
2.2: 4, 6*, 8*, 9, 10*,
12, 13, 14*
2.3: 2*, 3, 8*, 10*
2.4G: 2G, 4G, 8G, 10G
2.5G: 1G, 2G, 3G
3.1: 2,4*,5*,7,10*,11*
3.2: 1,3,4,5*,7*,8*,11
3.3: 2*,3,4*,6*,8G,9,14
3.4: 2*,4*,5,7G,8*
3.5: 2*,3,4,6*,8*, ,10G,11G
3.6: 2*,3,4*,5,6,8*
3.8: 2*,3,4*,6*, 7a*,7bG
3.9: page 175: 2*,4*; page 179:
20*,21*, 22*,26G
5.1: 1,2*,3,4*,6*,10*
5.2: 2*,3,4*,5,6*,7
5.3: 1,2*,3,4*,8*,12*,15G
5.4: 1,2*,3*,6*,7,9*
5.6: 1,2*,3*,5*,6*,7*,8G,
17*,18*,20*
5.7: 1,2*,3,4*,6*,7*,9*