Course Code	Semester	Course Name	LE/RC/LA	Course Type	Language of Instruction	ECTS
MCB1007 -	5	Introduction to Probability Theory and Statistics	4/0/0	CC	English	6

Course Goals	Upon completion of this course, students are expected to understand and apply basic concepts in probability theory and mathematical statistics.
Prerequisite(s)	NONE
Corequisite(s)	NONE
Special Requisite(s)	Read, understand, formulate, explain, and apply mathematical statements, and state and apply important results in key mathematical areas (Calculus I and Calculus II).
Instructor(s)	Assist. Prof. Dr. Emel Yavuz Duman
Course Assistant(s)	NONE
Schedule	Monday, 15:00-17:00, ZA-1; Friday, 13:00-15:00, ZA-1
Office Hour(s)	Thursday, 13:00-17:00, AK / 3-A-03/05
Teaching Methods and Techniques	Lectures and recitation.
Principle Sources	Lecture notes, http://web.iku.edu.tr/~eyavuz. I. Miller, M. Miller, John E. Freund's Mathematical Statistics with Applications, Pearson Prentice Hall, Seventh Edition, New Jersey, ISBN: 0978-0-13-124646-1, 2004.
Other Sources	Murray R. Spiegel, John J. Schiller, and R. Alu Srinivasan, Probability and Statistics, Schaum's Outline Series, Third Edition, New York, ISBN: 978-0-07-154426-9, 2009.

Course Schedules
Week	Contents	Learning Methods
1. Week	Sets, Combinatorial Methods, Binomial Coefficients	Lectures and recitation
2. Week	Sample Spaces, Event, The Probability of an Event, Some Rules of Probability	Lectures and recitation
3. Week	Conditional Probability, Independent Event, Bayes' Theorem	Lectures and recitation
4. Week	Random Variables, Discrete Probability Distributions	Lectures and recitation
5. Week	Continuous Random Variables	Lectures and recitation
6. Week	Multivariate Distributions	Lectures and recitation
7. Week	Marginal Distributions, Conditional Distributions	Lectures and recitation
8. Week	The Expected Value of a Random Variable, Moments	Lectures and recitation (Firts Midterm)
9. Week	Chebyshev’s Theorem, Moment Generating Functions	Lectures and recitation
10. Week	Product Moments, Conditional Expectation	Lectures and recitation
11. Week	The Discrete Uniform Distribution, The Bernoulli Distribution, The Binomial Distribution	Lectures and recitation (Second Midterm)
12. Week	The Negative Binomial and Geometric Distribution, The Hypergeometric Distribution	Lectures and recitation
13. Week	The Poisson Distribution, The Uniform Distribution	Lectures and recitation
14. Week	The Normal Distribution, The Normal Approximation to the Binomial Distribution, The Normal Approximation to the Poisson Distribution	Lectures and recitation
15. Week	Final week
16. Week	Final week
17. Week	Final week

Assessments
Evaluation tools	Quantity	Weight(%)
Midterm(s)	2	60
Final Exam	1	40

Program Outcomes PO-1 Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied information in these areas to model and solve engineering problems. PO-2 Ability to identify, formulate, and solve complex engineering problems; ability to select and apply proper analysis and modelling methods for this purpose. PO-3 Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way so as to meet the desired result; ability to apply modern design methods for this purpose. (Realistic constraints and conditions may include factors such as economic and environmental issues, sustainability, manufacturability, ethics, health, safety issues, and social and political issues according to the nature of the design.) PO-4 Ability to devise, select, and use modern techniques and tools needed for engineering practice; ability to employ information technologies effectively. PO-5 Ability to design and conduct experiments, gather data, analyse and interpret results for investigating engineering problems. PO-6 Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually. PO-7 Ability to communicate effectively, both orally and in writing; knowledge of a minimum of one foreign language. PO-8 Recognition of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself. PO-9 Awareness of professional and ethical responsibility. PO-10 Information about business life practices such as project management, risk management, and change management; awareness of entrepreneurship, innovation, and sustainable development. PO-11 Knowledge about contemporary issues and the global and societal effects of engineering practices on health, environment, and safety; awareness of the legal consequences of engineering solutions.

Learning Outcomes LO-1 Compute permutations and combinations. LO-2 Understand what a random variable is. LO-3 Define basic probability terminology, e.g., experiment, outcome, sample space, event, etc. LO-4 Describe a probability distribution and a probability density function. LO-5 Understand mathematical expectation LO-6 Explain joint, marginal and conditional probability distributions LO-7 Understand where/when special probability distribution functions should be used LO-8 Describe the various special continuous distributions. LO-9 Able to solve problems independently.

Course Assessment Matrix:

	PO 1	PO 2	PO 3	PO 4	PO 5	PO 6	PO 7	PO 8	PO 9	PO 10	PO 11