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Course Description Course Name : Probability Course Code : MT 261 Course Type : Compulsory Level of Course : First Cycle Year of Study : 2 Course Semester : Fall (16 Weeks) ECTS : 7 Name of Lecturer(s) : Prof.Dr. SADULLAH SAKALLIOĞLU Learning Outcomes of the Course : Explains Sample spaces, Sample points and Counting Rules Is able to solve the problems of permutations and combinations Uses Probability of an event, the Rules of Probability and Probability Axioms Applies conditional probability, independent events and Bayes theorem Knows the concept of a random variable and distribution of a random variable Knows the expected value, the variance and the properties of a random variable, Uses concepts of moments, skewness and kurtosi, and the Chebyshew inequality Knows somediscrete distributions (Bernoulli, binomial, polynomial, geometric, negative binomial) 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 basic concepts such as permutation, combination, probability theory, random variables and their distributions. This course forms the basis for introduction to statistics. Course Contents : Random experiment, sample space, event, probability function, probability calculations, conditional probability, random variables, functions of random variables, discrete random variables and their distributions. 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 The concept of sample space, sample point, event, counting rules for sample points Required reading Lecture, discussion and problem-solving 2 Permutations, circular permutations, combinations, Pascal´s triangle, repeated combinations Required reading Lecture, discussion and problem-solving 3 Ordered and unordered partitions, Binomial Theorem Required reading Lecture, discussion and problem-solving 4 The probability of an event, the probability axioms, some of the probability rules Required reading Lecture, discussion and problem-solving 5 Geometric probablity, Conditonal probability Required reading Lecture, discussion and problem-solving 6 Independent events, Bayes theorem Required reading Lecture, discussion and problem-solving 7 Random variables, probabilty distribution of discrete random variables Required reading Lecture, discussion and problem-solving 8 Mid-term exam Review of topics discussed in the lecture notes and sources Written exam 9 Probabilty distribution of continuous random variables Required reading Lecture, discussion and problem-solving 10 The expected value of a random variable, the variance and their properties, Required reading Lecture, discussion and problem-solving 11 Moments, skewness and kurtosis, Required reading Lecture, discussion and problem-solving 12 Chebyshew inequality, Problem solving Required reading Lecture, discussion and problem-solving 13 Bernoulli distribution, binomial distribution, a multinomial distribution, Geometric distribution Required reading Lecture, discussion and problem-solving 14 Negative binomial distribution, Hypergeometric distribution, Uniform distribution, Problem solving Required reading Lecture, discussion and problem-solving 15 Inroduction to continuous probabilty, solving problems Required reading Lecture, discussion and problem-solving 16/17 Final exam Review of topics discussed in the lecture notes and sources Written exam   Required Course Resources Resource Type Resource Name Recommended Course Material(s)  Akdeniz,F. (2010). Olasılık ve İstatistik , Nobel Kitabevi, Adana.  Gürsakal, N. (1997). Bilgisayar Uygulamalı İstatistik I,II, Marmara Kitabevi,Bursa.  McClave,J.T., Dietrich,F.H. And Sincich,T. (1997). Statistics,Prentice-Hall,Inc. Required Course Material(s)   Assessment Methods and Assessment Criteria Semester/Year Assessments Number Contribution Percentage     Mid-term Exams (Written, Oral, etc.) 1 100     Homeworks/Projects/Others 0 0 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 Is able to prove Mathematical facts encountered in secondary school. 4 2 Recognizes the importance of basic notions in Algebra, Analysis and Topology 3 3 Develops maturity of mathematical reasoning and writes and develops mathematical proofs. 5 4 Is able to express basic theories of mathematics properly and correctly both written and verbally 1 5 Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines. 3 6 Expresses clearly the relationship between objects while constructing a model 3 7 Draws mathematical models such as formulas, graphs and tables and explains them 3 8 Is able to mathematically reorganize, analyze and model problems encountered. 4 9 Knows at least one computer programming language 4 10 Uses effective scientific methods and appropriate technologies to solve problems 0 11 Knows programming techniques and is able to write a computer program 0 12 Is able to do mathematics both individually and in a group. 0 13 Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians 0 14 In addition to professional skills, the student improves his/her skills in other areas of his/her choice such as in scientific, cultural, artistic and social fields 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 4 56     Out of Class Study (Preliminary Work, Practice) 14 4 56 Assesment Related Works     Homeworks, Projects, Others 0 0 0     Mid-term Exams (Written, Oral, etc.) 1 25 25     Final Exam 1 30 30 Total Workload: 167 Total Workload / 25 (h): 6.68 ECTS Credit: 7