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İST 2011
MATHEMATICAL STATISTICS
Four hours lecture, Four credits
Instructors: Assist. Prof. Dr. Selma GÜRLER
E-Mail: [email protected]
Web Page: http://kisi.deu.edu.tr/selma.erdogan/
I.
PREREQUISITES :None
II.
MAIN TEXTBOOK
L. J. Bain and M. Engelhardt, Introduction to Probability and Mathematical
Statistics, 2nd Edition, Duxbury, 1992.
R. J. Larsen and M. L. Marx, An Introduction to Mathematical Statistics and Its
Applications, 3rd Edition, Prentice Hall.
III. SUPPLEMENTARY TEXTBOOK
J. E. Freund, Mathematical Statistics, 5th Edition, Prentice Hall.
IV.
COURSE OBJECTIVES
To provide a working knowledge of the mathematical tools, language, and
thought processes used by statisticians. To make you aware of the need for a
precise vocabulary in any academic discipline. To enable you to incorporate
statistical calculations into you're arsenal of problem solving techniques.
V.
COURSE OUTLINE
WEEK 1-2
1. Definition of Probability.
1.1 Some Properties of Probability
1.2. Conditional Probability and Independence
1.3. Combinatorial Methods
WEEK 3-4-5-6
2. Random Variables
2.1. Discrete Random Variables, Probability Mass Function and CDF
2.2. Continuous Random Variables, Probability Density Function and CDF
2.3. Some Properties of Expected Values
2.4 Moments and Moment Generating Functions
2.5. Special Discrete Distributions
2.6. Special Continuous Distributions
WEEK 7-8-9-10
3.
Joint Distributions
3.1. Marginal Distributions
3.2. Conditional distributions
3.3. Independent Random Variables
3.4. Properties of Random Variables
WEEK 11-12-13-14
4.
Functions of Random Variables
4.1. Transformation Methods
4.2. Sums of Random Variables
4.3. Order Statistics
4.4. Convergence of random variables
4.5. The Central Limit Theorem
VI.
SHORT COURSE OUTLINE
This course provides an introduction to theoretical and conceptual aspects of
Mathematical Statistics. Lectures will explain the theoretical origins and practical
implications of statistical concepts. Topics include: Probability, Conditional
probability and independence, Combinatorial problems, Random variables and
their distributions, Functions of random variables, Joint distributions, Expectation,
Conditional
expectation,
Moments
and
Moment
Convergence of random variables, Central limit theorem.
Generating
Functions,
VII. GRADING
Weekly homework will be given on material covered in class and may be
collected and graded on an unannounced basis.
Exam
Ratio
1st Midterm Exam
20%
2nd Midterm Exam
20%
Final Exam
50%
Class Participation /HW/Quiz
10%
Attendance is an essential requirement of this course and is the responsibility of
the student. Class begins promptly and you are expected to be present at the
beginning and at the end of each class session.