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Information
| Code | MT261 |
| Name | Probability |
| Term | 2023-2024 Academic Year |
| Semester | 3. Semester |
| Duration (T+A) | 4-0 (T-A) (17 Week) |
| ECTS | 7 ECTS |
| National Credit | 4 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. SADULLAH SAKALLIOĞLU |
| Course Instructor |
Prof. Dr. SADULLAH SAKALLIOĞLU
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
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 Content
Random experiment, sample space, event, probability function, probability calculations, conditional probability, random variables, functions of random variables, discrete random variables and their distributions.
Course Precondition
None
Resources
Olasılık ve İstatistik (Probability and Statistics), Fikri Akdeniz, Nobel Yayınevi, Adana
Notes
Lecture Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Understand Sample spaces, Sample points and Counting Rules |
| LO02 | Able to solve the problems of permutations and combinations |
| LO03 | Uses Probability of an event, the Rules of Probability and Probability Axioms |
| LO04 | Applies conditional probability, independent events and Bayes theorem |
| LO05 | Understand the concept of a random variable and distribution of a random variable |
| LO06 | Understand the expected value, the variance and the properties of a random variable, |
| LO07 | Uses concepts of moments, skewness and kurtosi, and the Chebyshew inequality |
| LO08 | Recognize some discrete distributions such as Bernoulli, Binomial, Multinomial, Geometric, Negative Binomial |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Comprehend the ability to prove the mathematical knowledge gained in secondary education on the basis of theoretical basis. | 4 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Understands importance of basic consepts of Algebra, Analaysis and Topology. | |
| PLO03 | Yetkinlikler - Öğrenme Yetkinliği | Mathematical reasoning demonstrates the ability to develop and write mathematical proofs by gaining maturity. | 5 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to express the basic theories of mathematics both correctly. | |
| PLO05 | Bilgi - Kuramsal, Olgusal | Understands the relationship between the different fields of mathematics and its relation to other disciplines. | 5 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Comprehends the ability to understand the relationships between the objects in the most understandable way while creating a model for any problem. | 5 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Comprehend and explain mathematical models such as formulas, graphs, tables and schema. | 4 |
| PLO08 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to mathematically rearrange, analyze, and model the problems they encounter. | 4 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Comprehends at least one of the computer programming languages. | |
| PLO10 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to use scientific methods and appropriate technologies effectively in problem solving. | 3 |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Understands sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians | |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | In addition to their professional development, they demonstrate their ability to continuously improve themselves by identifying their educational needs in scientific, cultural, artistic and social areas in line with their interests and abilities. | |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Understands the programming techniques and shows the ability to do programming. | |
| PLO14 | Yetkinlikler - Öğrenme Yetkinliği | Demonstrates the ability to study mathematics both independently and as a group. | 5 |
| PLO15 | Bilgi - Kuramsal, Olgusal | Demonstrate an awareness of the universal and social impacts and legal consequences of mathematical applications in the field of study. | 4 |
| PLO16 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to select, use and develop effectively for contemporary mathematical applications. | 3 |
| PLO17 | Bilgi - Kuramsal, Olgusal | It has ability of lifelong learning awareness, access to information, monitoring developments in science and technology and self-renewal ability. | 4 |
| PLO18 | Bilgi - Kuramsal, Olgusal | Gains the ability to use information technologies effectively for contemporary mathematical applications. | |
| PLO19 | Bilgi - Kuramsal, Olgusal | Gains the ability to design, conduct experiments, field work, data collection, analysis, archiving, text solving and / or interpretation according to mathematics fields. | 5 |
| PLO20 | Bilgi - Kuramsal, Olgusal | Gains the consciousness of prefesional ethics and responsibility. | 4 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | The concept of sample space, sample point, event, counting rules for sample points | Required reading | Öğretim Yöntemleri: Anlatım, Tartışma |
| 2 | Permutations, circular permutations, combinations, Pascals triangle, repeated combinations | Required reading | Öğretim Yöntemleri: Anlatım, Tartışma |
| 3 | Ordered and unordered partitions, Binomial Theorem | Required reading | Öğretim Yöntemleri: Anlatım, Tartışma |
| 4 | The probability of an event, the probability axioms, some of the probability rules | Required reading | Öğretim Yöntemleri: Anlatım, Tartışma |
| 5 | Geometric probablity, Conditonal probability | Required reading | Öğretim Yöntemleri: Anlatım, Tartışma |
| 6 | Independent events, Bayes theorem | Required reading | Öğretim Yöntemleri: Anlatım, Tartışma |
| 7 | Random variables, probabilty distribution of discrete random variables | Required reading | Öğretim Yöntemleri: Anlatım, Tartışma, Soru-Cevap |
| 8 | Mid-Term Exam | Written Exam | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Probabilty distribution of continuous random variables | Required reading | Öğretim Yöntemleri: Anlatım, Tartışma |
| 10 | The expected value of a random variable, the variance and their properties, | Required reading | Öğretim Yöntemleri: Anlatım, Tartışma |
| 11 | Moments, skewness and kurtosis, | Required reading | Öğretim Yöntemleri: Anlatım, Tartışma |
| 12 | Chebyshew inequality, Problem solving | Required reading | Öğretim Yöntemleri: Anlatım, Tartışma |
| 13 | Bernoulli distribution, binomial distribution, a multinomial distribution, Geometric distribution | Required reading | Öğretim Yöntemleri: Anlatım, Tartışma |
| 14 | Negative binomial distribution, Hypergeometric distribution, Uniform distribution, | Required reading | Öğretim Yöntemleri: Anlatım, Tartışma |
| 15 | Solving Problem | Review of topics discussed in the lecture notes and sources | Öğretim Yöntemleri: Tartışma, Soru-Cevap |
| 16 | Term Exams | Written exam | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Written exam | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 4 | 56 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 6 | 84 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 8 | 8 |
| Final Exam | 1 | 16 | 16 |
| Total Workload (Hour) | 164 | ||
| Total Workload / 25 (h) | 6,56 | ||
| ECTS | 7 ECTS | ||