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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.