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| IST2005 | Probability Theory | 4+0+0 | ECTS:6 | | Year / Semester | Fall Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT of STATISTICS and COMPUTER SCIENCES | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Prof. Dr. Zafer KÜÇÜK | | Co-Lecturer | None | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | To make students to understand the basics of mathematical background in probability, to describe some probability densities and to teach some inequalities. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | learn discrete and continous probability distributions | 4,8 | 1, | | LO - 2 : | calculate numerical characteristics of random varıables | 4,8 | 1, | | LO - 3 : | learn the importance of the characteristic and generating functions in the probability theory. | 4,8 | 1, | | LO - 4 : | have the ability of calculating the conditional expectation value of random variables | 4,8 | 1, | | LO - 5 : | learn limit theorems of the probability theory. | 4,8 | 1, | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), LO : Learning Outcome | | |
| Theory of Probability
Classification of distributions. Discrete distributions (Bernoulli, binomial, geometrical, negative binomial, Poisson, hypergeometrical).
Absolutely continuous distributions (uniform, normal, log-normal, exponentional, gamma, chi-square, Weibull, Cauchy, Laplace, Pareto).
Functions of random variables. Computer modeling of random variables. Kolmogorov's theorem.
Multidimensional distributions.
Conditional distributions. Independence of random variables.
Distributions of the sum, product and division of random variables.
Numerical characteristics of random variables (mathematical expectation, variance, standard derivation, moments)
Numerical characteristics of random variables (Mod, median, skewness and kurtosis, covariance, correlation coefficient) Markov's and Chebyshev's inequalities. Three sigmas law.Moment generating functions.
Characteristic functions.Types of convergences. Law of large numbers (Bernoulli, Poisson, Chebyshev, Markov, Khinchin theorems).Central limit theorem for the independent and identically distributed random variables.
Lindeberg and Lyapunov conditions.
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Classification of distributions. Basic examples about Discrete probation distributions (Bernoulli, binomial, geometrical, negative binomial, Poisson, hypergeometrical). | | | Week 2 | Basic examples about Absolutely continuous distributions (uniform, normal, log-normal, exponentional, gamma, chi-square, Weibull, Cauchy, Laplace, Pareto). | | | Week 3 | Distribution of function of random variable and examples. Computer modeling of random variable. Kolmogorov's theorem.
| | | Week 4 | Multidimensional distributions. | | | Week 5 | Conditional distribution. Independence of random variables. | | | Week 6 | Distributions of the sum, product and division of random variables. | | | Week 7 | Numerical characteristics of random variables (mathematical expectation, variance, standard derivation, moments) | | | Week 8 | Mid-term exam | | | Week 9 | Numerical characteristics of random variables (Mod, median, skewness and kurtosis, covariance, correlation coefficient) | | | Week 10 | Markov and Chebyshev's inequalities.Three sigmas law. | | | Week 11 | Moment generating functions. | | | Week 12 | Characteristic functions. | | | Week 13 | Types of convergences. Law of large numbers (Bernoulli, Poisson, Chebyshev, Markov, Khinchin theorems). | | | Week 14 | Types of convergences. Law of large numbers (Bernoulli, Poisson, Chebyshev, Markov, Khinchin theorems). | | | Week 15 | Central limit theorem for the independent and identically distributed random variables.Lindeberg and Lyapunov conditions. | | | Week 16 | End-of-term exam | | | |
| 1 | Akdeniz F. Olasılık ve İstatistik, Ankara Ü., Ankara, 1984, | | | 2 | Nasirova T., Khaniyev T. Yapar C., Ünver İ., Küçük Z. Olasılık. KTÜ Matbaası, Trabzon, 2009. | | | 3 | Shiryayev A.N. Probabilty.Springer-Verlag, 1984, | | | 4 | Feller W. An introduction to Probability Theory and its Applications. Vol.1, 2, John Wiley, New York, 1971. | | | |
| 1 | Ahmedova H. Olasılık teorisi ve matematiksel istatistik. Bakü, 2002. | | | 2 | Borovkov A.A. Olasılık teorisi. &1052;., Nauka, 2003, (Rusça) | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 09/11/2021 | 1,5 | 50 | | End-of-term exam | 16 | 30/12/2021 | 1,5 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 4 | 14 | 56 | | Sınıf dışı çalışma | 5 | 14 | 70 | | Laboratuar çalışması | 0 | 0 | 0 | | Arasınav için hazırlık | 10 | 1 | 10 | | Arasınav | 2 | 1 | 2 | | Uygulama | 0 | 0 | 0 | | Klinik Uygulama | 0 | 0 | 0 | | Ödev | 4 | 4 | 16 | | Proje | 0 | 0 | 0 | | Kısa sınav | 0 | 0 | 0 | | Dönem sonu sınavı için hazırlık | 20 | 1 | 20 | | Dönem sonu sınavı | 2 | 1 | 2 | | Diğer 1 | 0 | 0 | 0 | | Diğer 2 | 0 | 0 | 0 | | Total work load | | | 176 |
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