MATH 534: Mathematical Statistics I
Department of Applied Mathematics and Statistics, CSM
Fall 2013
Syllabus
Instructor: Dr. Amanda S. Hering
E-mail: ahering@mines.edu
Phone: 303.384.2462
Office: 235 Chauvenet Hall
Office Hours: M 10-11, T 10-11, R 10-11, F 10-11.
Course Description: The basics of probability, discrete and continuous probability distributions, sampling distributions, order statistics, convergence in probability and in
distribution, and basic limit theorems, including the central limit theorem, are covered.
Prereq: What it says on the AMS website: Consent of department. What you really need:
• Working knowledge of multivariate calculus, including but not limited to:
– Continuity and differentiation
– Multiple integration
– Power series
– Limits
– Taylor’s expansion
• An introductory statistics class that covered the following topics is also helpful:
– Random variables and probability distributions
– Normal distribution
– Expectation and variance
– Sample mean and its properties
– Student’s t-test
• Statistical or mathematical computing experience is not necessary and will rarely
be needed in this class.
Course Schedule: MWF 8-8:50am, Location Chauvenet Hall 143
Web Page: The username and password for the class website will be given in class.
http://inside.mines.edu/~ahering/math534/mathstat/
Textbook: (Required) Casella, G. and Berger, R. L. (2002) Statistical Inference, 2nd ed.,
Duxbury: Pacific Grove, CA.
http://www.amazon.com/Statistical-Inference-George-Casella/dp/0534243126
ISBN: 0-534-24312-6
Course Work: Your grade for the course will be based on the following (relative weights
given in percentage):
• Homework Assignments (25%): Homework assignments will be given approximately every week throughout the semester. Assignments will be collected at the
START of class on the due date. Late assignments will not be accepted.
• Exams (22.5%, 22.5%, and 30% each): There will be two midterm exams,
tentatively scheduled for Friday, October 4th and Friday, November 8th, each
worth 22.5%. There is a comprehensive final exam that is likely to be a takehome exam worth 30%.
The following letter grades are guaranteed:
A
B
C
D
F
100-90% 89-80% 79-70% 69-60% 59-0%
Exceptions: If you are unable to take an exam or complete an assignment on time due
to illness, accident, or circumstances beyond your control, please e-mail me within
24 hours of the exam or deadline so that appropriate arrangements can be made. If
you know ahead of time that you will have a university excused absence, homework
assignments are due before you leave, and exams will be made up after you return.
Policy on academic integrity/misconduct: The Colorado School of Mines affirms the
principle that all individuals associated with the Mines academic community have a
responsibility for establishing, maintaining an fostering an understanding and appreciation for academic integrity. In broad terms, this implies protecting the environment
of mutual trust within which scholarly exchange occurs, supporting the ability of the
faculty to fairly and effectively evaluate every students academic achievements, and
giving credence to the universitys educational mission, its scholarly objectives and the
substance of the degrees it awards. The protection of academic integrity requires there
to be clear and consistent standards, as well as confrontation and sanctions when individuals violate those standards. The Colorado School of Mines desires an environment
free of any and all forms of academic misconduct and expects students to act with
integrity at all times.
Academic misconduct is the intentional act of fraud, in which an individual seeks to
claim credit for the work and efforts of another without authorization, or uses unauthorized materials or fabricated information in any academic exercise. Student Academic
Misconduct arises when a student violates the principle of academic integrity. Such
behavior erodes mutual trust, distorts the fair evaluation of academic achievements,
violates the ethical code of behavior upon which education and scholarship rest, and
2
undermines the credibility of the university. Because of the serious institutional and individual ramifications, student misconduct arising from violations of academic integrity
is not tolerated at Mines. If a student is found to have engaged in such misconduct
sanctions such as change of a grade, loss of institutional privileges, or academic suspension or dismissal may be imposed. The complete policy is online.
Notes: A few more things...
• Check the website frequently for updates.
• I would like to know about any particular academic difficulties or personal problems that are affecting a student’s performance.
Student Learning Outcomes: At the conclusion of this class, students should be able to:
1. understand and apply the fundamentals of probability,
2. know how to perform basic operations on random variables, such as transformations, expectations, and moment generating functions,
3. identify and understand the appropriate use of common distributions,
4. handle multiple random variables and how to measure dependence among them,
5. apply convergence theorems to random samples, and
6. compute distributions of order statistics.
Course Outline: The list of topics on the following page are a rough outline of what will
be covered in this course:
3
Topic
1. Probability Theory
Set theory
Sample spaces and σ-algebras
Foundations of probability
Counting
Conditional probability
Independence
2. Random Variables
Random Variables
Distributions, pmf’s and pdf’s
Transformations
Expected values, variances, moments
Moment generating functions
3. Families of Distributions
Discrete distributions
Continuous distributions
Exponential family
Location and scale
4. Multiple Random Variables
Joint and marginal distributions
Conditional distributions and independence
Bivariate transformations
Covariance and correlation
Bivariate normal distribution
Hierarchical and mixture distributions
5. Random Samples
Random samples and statistics
Properties of sums, means, and moments
Order statistics
Statistical convergence theorems
4
Textbook Section
1.1
1.2
1.2
1.2
1.3
1.4
1.4
1.5, 1.6
2.1
2.2, 2.3
2.3
3.2
3.3
3.4
3.5
4.1
4.2
4.3
4.5
4.6
4.4
5.1
5.2, 5.3
5.4
5.5
2013 Tentative Semester Schedule
Monday
Wednesday
Aug 19th
Friday
Aug 21st
Aug 23rd
Aug 26th
Aug 28th
Aug 30th
Sep 2nd
Sep 4th
Sep 6th
Sep 11th
Sep 13th
Sep 18th
Sep 20th
Sep 25th
Sep 27th
Oct 2nd
Oct 4th
First Day of Class
Hmwk#1
Sep 9th
Hmwk#2
Sep 16th
Hmwk#3
Sep 23rd
Hmwk#4
Sep 30th
Exam #1
Oct 7th
Oct 9th
Oct 11th
Oct 16th
Oct 18th
Oct 23rd
Oct 25th
Oct 30th
Nov 1st
Nov 6th
Nov 8th
Hmwk#5
Oct 14th
Fall Break
Hmwk#6
Oct 21st
Hmwk#7
Oct 28th
Hmwk#8
Nov 4th
Exam #2
Nov 11th
Nov 13th
Nov 15th
Nov 20
Nov 22th
Hmwk#9
Nov 18th
Hmwk#10
Nov 25th
Nov 27th
Thanksgiving
Dec 2nd
Last Class
Dec 9th
Final Exams
Nov 29th
Thanksgiving
Dec 4th
Hmwk#11
Dec 11th
Final Exams
5
Dec 6th
Dec 13th