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Course Description Course Name : Theory of Probability Course Code : ISB-537 Course Type : Compulsory Level of Course : Second Cycle Year of Study : 1 Course Semester : Fall (16 Weeks) ECTS : 6 Name of Lecturer(s) : Asst.Prof.Dr. GÜLESEN ÜSTÜNDAĞ ŞİRAY Learning Outcomes of the Course : Define the basic principles of probability calculations. Understand the axioms of probability and show how to use them. Use the concepts of conditional probability and independency. Obtain the expected value and variance of a random variable. Obtain the moment generating of a random variable. Use Chebyshev´s and Jensen´s inequality. Find the distribution function of a random variable. Learn some special distributions. Find the distributions of the functions of random variables. Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : None Recommended Optional Programme Components : None Aim(s) of Course : To teach the basic principles of probability theory Course Contents : The course covers the following items: probability,discrete and continious types random variables, properties of the distribution functions, multivariate distributions, some special distributions, distributions of functions of random variables Language of Instruction : Turkish Work Place : Seminar room of the department   Course Outline /Schedule (Weekly) Planned Learning Activities Week Subject Student's Preliminary Work Learning Activities and Teaching Methods 1 Probability, discrete and continious types random variables, properties of the distribution function Reading the related references Lecture, discussion, problem-solving 2 Expectation of a random variable, some special expectations, Chebyshev´s inequality Reading the related references Lecture, discussion, problem-solving 3 Distributions of two random variables, conditional distributions and expectations, the correlation coefficient Reading the related references Lecture, discussion, problem-solving 4 Independent random variables, extension to several random variables Reading the related references Lecture, discussion, problem-solving 5 Discrete type distributions, Uniform, Bernoulli, Binom and related distributions Reading the related references Lecture, discussion, problem-solving 6 Continious type distributions, Uniform, gamma, exponential and chi-square distributions Reading the related references Lecture, discussion, problem-solving 7 Normal and bivariate normal distributions Reading the related references Lecture, discussion, problem-solving 8 Mid-Term Exam Review the topics discussed in the lecture notes and sources Written Exam 9 Transformations of variables of discrete and continious types Reading the related references Lecture, discussion, problem-solving 10 Distribution of functions of random vaiables Reading the related references Lecture, discussion, problem-solving 11 Change of variable technique Reading the related references Lecture, discussion, problem-solving 12 The Beta, t and F distributions Reading the related references Lecture, discussion, problem-solving 13 The moment-generating function technique Reading the related references Lecture, discussion, problem-solving 14 Distribution of sample mean and sample variance Reading the related references Lecture, discussion, problem-solving 15 Expectations of functions of random variables Reading the related references Lecture, discussion, 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)  Hogg,R.V. And Craig, A.T. (2005). Introduction to Mathematical Statistics. Prentice Hall, Sixth Edition.  Akdi, Y. (2010). Matematiksel İstatistiğe Giriş , Gazi Kitabevi, ANKARA.  Casella, G. and Berger, R.L. (2002). Statistical Inference. Duxbury, Second Edition. Required Course Material(s)   Assessment Methods and Assessment Criteria Semester/Year Assessments Number Contribution Percentage     Mid-term Exams (Written, Oral, etc.) 1 60     Homeworks/Projects/Others 5 40 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 Possess advanced level of theoretical and applicable knowledge in the field of Probability and Statistics. 5 2 Conduct scientific research on Mathematics, Probability and Statistics. 3 3 Possess information, skills and competencies necessary to pursue a PhD degree in the field of Statistics. 4 4 Possess comprehensive information on the analysis and modeling methods used in Statistics. 2 5 Present the methods used in analysis and modeling in the field of Statistics. 2 6 Discuss the problems in the field of Statistics. 4 7 Implement innovative methods for resolving problems in the field of Statistics. 4 8 Develop analytical modeling and experimental research designs to implement solutions. 1 9 Gather data in order to complete a research. 4 10 Develop approaches for solving complex problems by taking responsibility. 2 11 Take responsibility with self-confidence. 3 12 Have the awareness of new and emerging applications in the profession 1 13 Present the results of their studies at national and international environments clearly in oral or written form. 0 14 Oversee the scientific and ethical values during data collection, analysis, interpretation and announcment of the findings. 0 15 Update his/her knowledge and skills in statistics and related fields continously 0 16 Communicate effectively in oral and written form both in Turkish and English. 0 17 Use hardware and software required for statistical applications. 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 3 42     Out of Class Study (Preliminary Work, Practice) 14 2 28 Assesment Related Works     Homeworks, Projects, Others 5 8 40     Mid-term Exams (Written, Oral, etc.) 1 10 10     Final Exam 1 20 20 Total Workload: 140 Total Workload / 25 (h): 5.6 ECTS Credit: 6