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Course Description Course Name : Probability Theory Course Code : İSB203 Course Type : Compulsory Level of Course : First Cycle Year of Study : 2 Course Semester : Fall (16 Weeks) ECTS : 6 Name of Lecturer(s) : Assoc.Prof.Dr. ALİ İHSANGENÇ Learning Outcomes of the Course : Learns the definitions of sigma algebra, algebra, Borel algebra, measure and probability. Learns the definitions of measurable spaces and probability spaces and knows where to use. Learns measurable functions, random variables, distribution functions and its properties. Learns discrete random variables, probability mass functions, continuous random variables, probability density function and their properties. Learns the expected value of a random variable, expectation of a function of a random variable, variance, moments and their properties. Learns Chebyshev and some other moment inequalities. Learns moment generating functions, probability generating functions and characteristic function. Learns percentiles of a random variable. Learns some named distributions, exponential families, location-scale families. 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 the axiomatic probability and its consequences which constitute a basement for the theory of statistics. Course Contents : Probability definitions, sigma algebra, axiomatic probability, consequences of axiomatic probability, conditional probability, random variables and their properties, expected value, mode, median, distributions and their properties. 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 Sigma algebra, algebra, Borel algebra, probability Source reading Lecture, discussions and problem solving 2 Measurable spaces, measure spaces, probability spaces and their properties Source reading Lecture, discussions and problem solving 3 Measurable functions, random variables, distribution functions and their properties Source reading Lecture, discussions and problem solving 4 Discrete random variables, probability mass function, continuous random variables, probability density function Source reading Lecture, discussions and problem solving 5 Expectation of a random variable, variance and moments Source reading Lecture, discussions and problem solving 6 Chebyshev and some other moment inequalities Source reading Lecture, discussions and problem solving 7 Moment generating function, probability generating function, product moments, characteristic function Source reading Lecture, discussions and problem solving 8 Mid-term exam Review the topics discussed in the lecture notes and sources Written exam 9 Percentiles Source reading Lecture, discussions and problem solving 10 Discrete probability distributions: uniform, Bernoulli and binomial Source reading Lecture, discussions and problem solving 11 Geometric, negative binomial, Poisson and hypergeometric distributions Source reading Lecture, discussions and problem solving 12 Continuous probability distributions: Uniform, gamma, exponential and chi-square Source reading Lecture, discussions and problem solving 13 Beta, normal, log-normal, Cauchy, Laplace, Weibull, t and F distributions Source reading Lecture, discussions and problem solving 14 Exponential families Source reading Lecture, discussions and problem solving 15 Exponential families and location-scale families Source reading Lecture, discussions 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)   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 2 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 0 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