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Course Description Course Name : Theory of Statistics Course Code : İSB204 Course Type : Compulsory Level of Course : First Cycle Year of Study : 2 Course Semester : Spring (16 Weeks) ECTS : 6 Name of Lecturer(s) : Assoc.Prof.Dr. ALİ İHSANGENÇ Learning Outcomes of the Course : Makes manipulations with random vectors and their distributions. Finds moment generating function and characteristic function of a random vector. Finds the distribution of a function of random vectors. Finds the distributions of sample statistics. Learns the methods of point estimation. Learns the properties of a point estimator and how to compare candidate estimators. Learns marginal and conditional distributions. Learns stochastic independence. Learns the concepts of covariance and correlation. Learns order statistics. Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : None Recommended Optional Programme Components : None Aim(s) of Course : This course aims to give basic mathematical statistics concepts and their connections with the real world problems. Course Contents : Random vectors, functions of random vectors and their distributions, conditional distributions, independence, covariance, correlation, random sample, order statistics, parameter estimation, properties of a point estimator Language of Instruction : Turkish Work Place : Faculty of Arts and Sciences Annex classrooms   Course Outline /Schedule (Weekly) Planned Learning Activities Week Subject Student's Preliminary Work Learning Activities and Teaching Methods 1 Random vectors, joint probability mass function, joint probability density function Source reading Lecture, discussion and problem solving 2 Expectation of a random vector, variance-covariance vector Source reading Lecture, discussion and problem solving 3 Marginal and conditional distributions, conditional expectation Source reading Lecture, discussion and problem solving 4 Covariance and correlation Source reading Lecture, discussion and problem solving 5 Functions of a random vectors and their distributions Source reading Lecture, discussion and problem solving 6 Method of transformation and method of moment generating function Source reading Lecture, discussion and problem solving 7 Random samples, distribution of sample statistics, sampling from a normal distribution Source reading Lecture, discussion and problem solving 8 Mid-term exam Review the topics discussed in the lecture notes and sources Written exam 9 Sample mean and its distribution Source reading Lecture, discussion and problem solving 10 Order statistics and related statistics Source reading Lecture, discussion and problem solving 11 Point estimation methods, method of moments Source reading Lecture, discussion and problem solving 12 Maximum likelihood estimation, method of least squares Source reading Lecture, discussion and problem solving 13 Properties of point estimators, unbiasedness, efficiency, consistency, sufficiency Source reading Lecture, discussion and problem solving 14 Asymptotic properties, convergence in probability, weak law of large numbers, almost surely convergence, strong law of large numbers Source reading Lecture, discussion and problem solving 15 Convergence in distribution, Central Limit Theorem, convergence in moments Source reading Lecture, discussion and problem solving 16/17 Final exam Review the topics discussed in the lecture notes and sources Written exam   Required Course Resources Resource Type Resource Name Recommended Course Material(s)  Casella, G. and Berger, R.L. (2002). Statistical Inference. Duxbury, Second Edition.  Miller, I and Miller, M. (2004). John E. Fredund’s Mathematical Statistics with Applications , Pearson Prentice Hall, Seventh Edition. Required Course Material(s)  Öztürk, F., Akdi, Y., Aydoğdu, H. ve Karabulut, İ. (2006), Parametre tahmini ve hipotez testi, Bıçaklar Kitabevi.  Akdi, Y. (2005) Matematiksel İstatistiğe Giriş, Bıçaklar Kitabevi.   Assessment Methods and Assessment Criteria Semester/Year Assessments Number Contribution Percentage     Mid-term Exams (Written, Oral, etc.) 1 80     Homeworks/Projects/Others 5 20 Total 100 Rate of Semester/Year Assessments to Success 40   Final Assessments 100 Rate of Final Assessments to Success 60 Total 100   Contribution of the Course to Key Learning Outcomes # Key Learning Outcome Contribution* 1 Utilize computer systems and softwares 0 2 Apply the statistical analyze methods 5 3 Make statistical inference(estimation, hypothesis tests etc.) 5 4 Generate solutions for the problems in other disciplines by using statistical techniques 4 5 Discover the visual, database and web programming techniques and posses the ability of writing programme 0 6 Construct a model and analyze it by using statistical packages 0 7 Distinguish the difference between the statistical methods 5 8 Be aware of the interaction between the disciplines related to statistics 2 9 Make oral and visual presentation for the results of statistical methods 0 10 Have capability on effective and productive work in a group and individually 0 11 Develop scientific and ethical values in the fields of statistics-and scientific data collection 0 12 Explain the essence fundamentals and concepts in the field of Probability, Statistics and Mathematics 5 13 Emphasize the importance of Statistics in life 3 14 Define basic principles and concepts in the field of Law and Economics 0 15 Produce numeric and statistical solutions in order to overcome the problems 5 16 Construct the model, solve and interpret the results by using mathematical and statistical tehniques for the problems that include random events 5 17 Use proper methods and techniques to gather and/or to arrange the data 5 18 Professional development in accordance with their interests and abilities, as well as the scientific, cultural, artistic and social fields, constantly improve themselves by identifying training needs 0 * Contribution levels are between 0 (not) and 5 (maximum).   Student Workload - ECTS Works Number Time (Hour) Total Workload (Hour) Course Related Works     Class Time (Exam weeks are excluded) 14 4 56     Out of Class Study (Preliminary Work, Practice) 14 4 56 Assesment Related Works     Homeworks, Projects, Others 5 5 25     Mid-term Exams (Written, Oral, etc.) 1 10 10     Final Exam 1 15 15 Total Workload: 162 Total Workload / 25 (h): 6.48 ECTS Credit: 6