Counting techniques, combinatorial methods, random experiments, sample spaces, events, probability axioms, some rules of probability, conditional probability, independence, Bayes' theorem, random variables (r.v.'s), probability distributions, discrete and continuous r.v.'s, probability density functions, multivariate distributions, marginal and conditional distributions, expected values, moments, conditional expectation, Chebyshev's theorem, product moments, moments of linear combinations of r.v.'s, special discrete distributions, uniform, Bernoulli, binomial, negative binomial, geometric, hypergeometric and Poisson distributions, special probability densities, uniform, gamma, exponential and normal densities, normal approximation to binomial, distribution of functions of r.v.'s, distribution function and moment-generating law of large numbers, the central limit theorem, function techniques, distribution of the mean, basic methods for statistical estimation and hypothesis testing.
Introduction to Probability (MATH 203)
| Programs\Type | Required | Core Elective | Area Elective |
| Computer Science and Engineering | * | ||
| Computer Science and Engineering | * | ||
| Data Science and Analytics | * | ||
| Economics | * | ||
| Economics | * | ||
| Electronics Engineering | * | ||
| Electronics Engineering | * | ||
| Industrial Engineering | * | ||
| Industrial Engineering (Previous Name: Manufacturing Systems Engineering) | * | ||
| International Studies | * | ||
| International Studies | * | ||
| Materials Science and Nano Engineering | * | ||
| Materials Science and Nano Engineering (Previous Name: Materials Science and Engineering) | * | ||
| Mathematics Minor | * | ||
| Mechatronics Engineering | * | ||
| Mechatronics Engineering | * | ||
| Microelectronics | * | ||
| Molecular Biology, Genetics and Bioengineering | * | ||
| Molecular Biology, Genetics and Bioengineering (Pre. Name: Biological Sciences and Bioengineering) | * | ||
| Political Science | * | ||
| Political Science (Previous Name: Social and Political Sciences) | * | ||
| Telecommunications | * |
CONTENT
OBJECTIVE
- To give an understanding of uncertainty and randomness
- To teach the fundemantal concepts and defintions of probability
- To equip the students with the tools and techniques of probability theory
LEARNING OUTCOMES
- Use the basic principles of counting, permutations, combinations, and multinomial coefficients.
- Perform set operations and compute elementary (conditional) probabilities.
- Use the concept of random variables and their distributions, cumulative distribution functions.
- Compute marginal distributions, conditional distributions and conditional expectations.
- Evaluate mathematical expectations, moments, variances, co-variances, conditional expectations, and moment-generating functions.
- Investigate the basic properties of important discrete and continuous random variables such as Bernouilli, binomial, hypergeometric, Poisson, uniform, exponential, gamma and normal.
- Implement different techniques such as the distribution function technique, the moment generating function technique to evaluate the distribution of functions of random variables.
- Investigate the properties of various statistics (eg. sample mean, sample variance, order statistics) and use them in simple statistical estimation and hypothesis testing problems.
- Applications in various disciplines.
PROGRAMME OUTCOMES
1. Understand the world, their country, their society, as well as themselves and have awareness of ethical problems, social rights, values and responsibility to the self and to others. 2
2. Understand different disciplines from natural and social sciences to mathematics and art, and develop interdisciplinary approaches in thinking and practice. 4
3. Think critically, follow innovations and developments in science and technology, demonstrate personal and organizational entrepreneurship and engage in life-long learning in various subjects; have the ability to continue to educate him/herself. 4
4. Communicate effectively in Turkish and English by oral, written, graphical and technological means. 3
5. Take individual and team responsibility, function effectively and respectively as an individual and a member or a leader of a team; and have the skills to work effectively in multi-disciplinary teams. 3
1. Possess sufficient knowledge of mathematics, science, fundamental engineering, computational methods and program-specific engineering topics; use theoretical and applied knowledge of these areas in complex engineering problems. 4
2. Identify, define, formulate and solve complex engineering problems while considering the UN Sustainable Development Goals; choose and apply suitable analysis, design, estimation/prediction and modeling methods for this purpose. 3
3. Develop, choose and use modern techniques and tools that are needed for analysis and solution of complex problems faced in engineering applications; use information technologies effectively. 2
4. Have the ability to design a complex system, process, instrument or a product under realistic constraints and conditions, with the goal of fulfilling creative current and future requirements. 2
5. Use research methods, including conducting literature reviews, designing experiments, performing experiments, collecting data, analyzing results, and interpreting results, to investigate complex engineering problems or discipline-specific research topics. 2
6. Possess knowledge of business practices such as project management, risk management, change management, and economic feasibility analysis; awareness on entrepreneurship and innovation. 1
7. Possess knowledge of impact of engineering solutions on society, health and safety, the economy, sustainability, and the environment within the framework of the UN Sustainable Development Goals; awareness on legal outcomes of engineering solutions; awareness of acting impartially and inclusively without any form of discrimination; act in accordance with ethical principles, possessing knowledge of professional and ethical responsibilities. 1
8. Communicate effectively, both orally and in writing, on technical subjects, considering the diverse characteristics of the target audience (such as education, language, and profession). 2
1. Provide constructive analysis of economic phenomena at the national and international level, and interactions between the two. 1
2. Develop an understanding of organizations and institutions in the society as well as their influence on the economy. 1
3. Recognize how incentives shape the behavior of individuals and organizations. 1
4. Identify "economic" problems and propose alternative models and/or design and conduct research to provide viable solutions using theoretical tools and/or quantitative methods. 1
5. Communicate problems and solutions to managerial and policy decision-making units as well as to lay audiences. 1
1. Analyze global affairs from international relations and economics perspectives. 1
2. Demonstrate theoretical and practical knowledge of the international affairs. 1
3. Compete for increasing opportunities in careers within the newly emerging global institutions. 1
4. Evaluate the international political events and present their views and positions on international affairs with advanced oral and written skills. 1
1. Understand and follow changes in patterns of political behavior, ideas and structures. 1
2. Develop the ability to make logical inferences about social and political issues on the basis of comparative and historical knowledge. 1
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ASSESSMENT METHODS and CRITERIA
| Percentage (%) | |
| Final | 45 |
| Midterm | 50 |
| Quiz | 10 |
RECOMENDED or REQUIRED READINGS
| Textbook |
John Freund’s Mathematical Statistics with Applications, 8th Edition, Pearson-Prentice Hall, 2004, ISBN 978-1-292-02500-1. |
| Optional Readings |
Supplementary Texts : |