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Course Description Course Name : Mathematical Statistics I Course Code : IEM 732 Course Type : Optional Level of Course : Second Cycle Year of Study : 1 Course Semester : Fall (16 Weeks) ECTS : 6 Name of Lecturer(s) : Asst.Prof.Dr. EBRU ÖZGÜR GÜLER Learning Outcomes of the Course : Explains basic probability concepts. Knows mathematical and statistical properties of discrete and continuous random variables. Models real life data by using discrete and continuous random variables. Understands the foundations of the estimation theory and its applications in real life. Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : None Recommended Optional Programme Components : None Aim(s) of Course : The objective of this course is to understand techniques and basic results of probability and mathematical statistics. Basic concepts of probability and its applications to real life data through random variables are explained. Mathematical and statistical properties of discrete and continuous random variables are investigated. Estimation methods are explained briefly. Moment generating functions are also explained in this course. Course Contents : The content of this course covers probability, discrete random variables, continuous random variables with mathematical and statistical properties of these topics, and the maximum likelihood estimation. Language of Instruction : Turkish Work Place : Classroom   Course Outline /Schedule (Weekly) Planned Learning Activities Week Subject Student's Preliminary Work Learning Activities and Teaching Methods 1 Basic concepts, methods of enumeration Chapter 1, pp.1-18 Lecture 2 Conditional probability, independent events, Bayes´ theorem Chapter 1, pp.18-39 Lecture 3 Discrete probability distributions, and their expectations Chapter 2, pp.40-59 Lecture 4 Special discrete distributions, estimation Chapter 2, pp.59-79 Lecture, package program 5 Special discrete distributions, estimation Chapter 2, pp.59-79 Lecture,software package 6 Linear functions of independent random variables, multivariate discrete distributions Chapter 2, pp.79-96 Lecture 7 General review Review of Chapter 1 ve and Chapter 2 Problem session, discussion 8 Midterm exam 9 Continuous Distributions: Descriptive statistics and exploratory data analysis Chapter 3, pp.97-112 Lecture, software package 10 Continuous Distributions: Descriptive statistics and exploratory data analysis Chapter 3, pp.97-112 Lecture, software package 11 Continuous probability distributions and some special continuous distributions Chapter 3, pp.112-126 Lecture 12 Continuous probability distributions and some special continuous distributions Chapter 3, pp.112-126 Lecture 13 The normal distribution and the estimation in the continuous case Chapter 3, pp.126-142 Lecture, software package 14 The central limit theorem and approximations for discrete distributions Chapter 3, pp.142-154 Lecture 15 Moments and moment generating functions Chapter 6.1, pp.295-306 Lecture 16/17 Final exam   Required Course Resources Resource Type Resource Name Recommended Course Material(s)  A Brief Course in Mathematical Statistics", Elliot A. Tanis ve Robert V. Hogg, Pearson, 2008. Required Course Material(s)   Assessment Methods and Assessment Criteria Semester/Year Assessments Number Contribution Percentage     Mid-term Exams (Written, Oral, etc.) 1 50     Homeworks/Projects/Others 2 50 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 Explains Econometric concepts 3 2 Equipped with the foundations of Economics, develops Economic models 3 3 Models problems using the knowledge of Mathematics, Statistics, and Econometrics 5 4 Acquires the ability to analyze, benchmark, evaluate and interpret at conceptual levels to develop solutions to problems 4 5 Collects, edits, and analyzes data 5 6 Uses advanced software packages concerning Econometrics, Statistics, and Operation Research 3 7 Develops the ability to use different resources in an area which has not been studied in the scope of academic rules, synthesizes the information gathered, and gives effective presentations 0 8 Speaks Turkish and at least one other foreign language in accordance with the requirements of academic and business life. 4 9 Questions traditional approaches and their implementation and develops alternative study programs when required 1 10 Recognizes and implements social, scientific, and professional ethic values 0 11 Gives a consistent estimate for the model and analyzes and interprets its results 5 12 Takes responsibility individually and/or as a member of a team; leads a team and works effectively 4 13 Defines the concepts of statistics, operations research and mathematics. 4 14 Knowing the necessity of life-long learning, follows the latest developments in the field of study and improves himself continiously 1 15 Follows the current issues, and interprets the data about economic and social events. 3 16 Understands and interprets the feelings, thoughts and behaviours of people and expresses himself/herself orally and in written form efficiently 3 * 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 3 42     Out of Class Study (Preliminary Work, Practice) 14 4 56 Assesment Related Works     Homeworks, Projects, Others 2 8 16     Mid-term Exams (Written, Oral, etc.) 1 12 12     Final Exam 1 14 14 Total Workload: 140 Total Workload / 25 (h): 5.6 ECTS Credit: 6