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).
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.
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.