Department of Mathematics and Physics
College of Arts and Sciences
University of Qatar
Course Syllabus
Components
STAT 351
Mathematical Statistics
Spring 2010
By
Adil Yousif, Ph. D.
Introduction to Probability
Adil Yousif
Course Information
Course Name: Mathematical Statistics
Course Number: STAT 351
Credit Hours: 3 Credit hrs
Prerequisites: STAT 251.
Required Textbook: Miller, I & Mille: Freund’s Mathematical Statistics, 7th Ed., Prentice
Hall Inc. Upper Saddle River, NJ 07458, ISBN 0-13-123613-X, (1999)
Faculty Information
Name: Adil Yousif, Ph. D.
Program: Statistics
Telephone: 4852163
E- Mail: aeyousif@qu.edu.qa
Website: http://faculty.qu.edu.qa/ayousif/
Office Number: 207E (Corridor 5)
Office Hours: 10:00 -11:00 a.m. (Mon., Wed., & Thurs) or by appointment
Course Description
2
 Sampling Distributions: Distribution of mean and variance. t,  , and F distributions.
Central limit theorem.
 Theory of Point Estimation: Unbiasedness. Consistency. Sufficiency. Exponential
family of distributions. Completeness. Uniformly minimum variance unbiased estimation.
Lower bounds of the variance of unbiased estimators. Information. Efficiency of an
estimator.
 Methods of Estimation: Maximum likelihood method. Moments' method. Least
squares method.
 Introduction to interval estimation: Pivotal quantity. A General method for
confidence intervals. Large sample confidence interval.
 Test of hypotheses: Basic concepts. Most powerful test. Neyman-Pearson lemma.
Uniformly most powerful test. Uniformly most powerful unbiased test. Likelihood ratio
test. Sequential tests.
 Introduction to the Bayesian Method of estimation: Basic concepts. Point estimates.
Interval estimation. Bayesian method in hypotheses testing.
Course Objectives

To acquaint students with some basic statistical tools needed to develop some
statistical theorems and applications.
Course Syllabus Components
-1-
Academic Year 2008/2009
Mathematical Statistics
Adil Yousif


To familiarize students with methods of statistical inference under various probability
models and how to apply them.
To broaden the foundation of the student to be ready for advanced probability courses.
Student Learning Outcomes





Enable students to understand tools need to develop theoretical statistics.
Students will be familiarized with different probability models.
Students will be able to understand and implement basic statistical inference
techniques.
Students will be able to recognize basic sampling distributions.
Students will be familiarized with introductory Bayesian statistics.
Content Distribution
Topics
Weeks
Revision of Probability Distribution and Densities
Chapter 7: Functions of Random Variables
Assignments
1
2-3
Chapter 8: Sampling Distribution, Chi-square, t-Distribution, FDistribution and order statistics.
Assignments
1&2
Assignment 3
4-7
Test 1
Chapter 10: Point Estimation, Unbiasness, Efficiency, Sufficiency,
Consistency, m.l.e. and Bayesian Estimation.
Chapter 11, Interval Estimation
8-10
Assignment 4
Assignment 5
10-11
Test II
Chapter 12 & 13: Testing Hypotheses Involving Mean, Variance and
Proportions.
Final Exam (comprehensive)
12-13
Assignment 6
14
Final
Delivery Methods




Class participation is encouraged and may be assessed for extra credit.
Small group during in-class assignment is encouraged to emphasize learning from and
with others (pears education philosophy).
H. W. is encouraged to be discussed in groups however individual responsibility and
presentation of one or two problems in class are expected.
Students should visit the Blackboard (Bb) on regular bases for more instructions and
materials. (assignment will be displayed on Bb only)
Learning Resources and Media
The primarily resources for this course are:
 The Text Book
 The classroom notes and materials passed out in class
 Material displayed in the Bb
 References listed at the end of this syllabus
Course Syllabus Components
-2-
Academic Year 2009/2010
Mathematical Statistics
Adil Yousif
Assessment Policy and Tools
The course evaluation will be based on two tests (20% each), a comprehensive final
(40%), quizzes (10%), homework and in-class assignments (10%).Homework
assignments will be given occasionally and collected in class on the due date.
A letter grade will be assigned based on the following scale
Percent Grading Scale
90 - 100
85 - 89
80 – 84
75 - 79
70 – 74
65 – 69
60 - 64
59 - 0
Letter Grad
A
B+
B
C+
C
D+
D
F
Final Exam and Tests:
Test I
Test II
Wednesday, June 9, 2010, at 8:00 – 10:00 a.m.
Monday, March 29, 2010
Monday, May 03, 2010
Final Exam
Matrix of Objectives and Outcomes
OBJECTIVES
To acquaint students with
some basic statistical tools
needed to develop some
statistical theorems and
applications
To familiarize students with
methods of statistical inference
under various probability
models and how to apply
them.
To broaden the foundation of
the student to be ready for
advanced probability courses.
Course Syllabus Components
LEARNING OUTCOMES


Assessment
Tools
Exams
Enable
students
to Assignments
understand tools need to
develop
theoretical
statistics.
Students
will
be
familiarized
with
different
probability
models.
Exams
Assignments
Students will be able to
understand and implement
basic statistical inference
techniques.
 Students will be able to Exams
recognize
basic Assignments
sampling distributions.
-3-
Academic Year 2009/2010
Mathematical Statistics
Adil Yousif
Assignments Rubric
Total Score (20)
CATEGORY
Organization
Information is very
organized with
well-constructed
paragraphs and
subheadings.
4
Information is
organized with
well-constructed
paragraphs.
3
2
Information is
organized, but
paragraphs are not
well-constructed.
1
Amount of
Information
All topics are
addressed and all
questions
answered with at
least 2 sentences
about each.
All topics are
addressed and
most questions
answered with at
least 2 sentences
about each.
All topics are
addressed, and
most questions
answered with 1
sentence about
each.
One or more topics
were not
addressed.
Mechanics
No grammatical,
spelling or
punctuation errors.
Almost no
grammatical,
spelling or
punctuation errors
A few grammatical
spelling or
punctuation errors.
Many grammatical,
spelling, or
punctuation errors.
Diagrams &
Illustrations
Diagrams and
illustrations are
neat, accurate and
add to the reader's
understanding of
the topic.
Diagrams and
illustrations are
accurate and add
to the reader's
understanding of
the topic.
Diagrams and
illustrations are
neat and accurate
and sometimes
add to the reader's
understanding of
the topic.
Diagrams and
illustrations are not
accurate OR do not
add to the reader's
understanding of
the topic.
The information
appears to be
disorganized. 8)
Test Policy:
Tests will be administered on the schedule dates as posted in the syllabus unless the whole
class agreed and signed a sheet to change the test date for a period of one week within the
posted date. No make up exam under any condition. If a student misses a test and provides
documents for genuine reasons the percentage of that test will be distributed over other tests,
(class work, home work assignments and lab project will not get part of these points). If a
student shows continuous progress through out the semester, the higher scores towards the
ends may get extra weights.
If you have a preplanned trip overlapping with a test date e-mail me a description of the trip,
phone calls are NOT accepted.
Course Syllabus Components
-4-
Academic Year 2009/2010
Mathematical Statistics
Adil Yousif
Learning Activities and Tasks
Students should be held responsible for their own ongoing learning process such as: class
attendance, Homework assignments and lab assignments, Final Project, Presentation, Tests
and Final Exam.
Regulations




Attendance is mandatory and students with absence of more than 25% will be
deprived from taking final exam which result in a failing grade.
Plagiarism and cheating are not tolerated and any student caught will be subject to the
university regulations;
Late or missed assignments will have a zero score;
Using of cell phones in class is prohibited and may results in dismissal from class.
P.S. Students with special needs are eligible for further help according to their needs.
Please arrange with me if you need such help
References and Additional Resources
1. Introduction to Probability, Hog and Crag
2. Introduction to Statistics and Probability, Mood and Grabble
3. Mathematical Statistics With Application, Wackerly, Mendenhall, and Schaeffer
Course Syllabus Components
-5-
Academic Year 2009/2010