This course is designed to serve the following objectives:
(a) To motivate the students for use of probabilistic models in engineering analysis and design
(b) To equip the students with the basics of probability theory
(c) To introduce random signal and random process concepts.
Prerequisite(s)
NONE
Corequisite(s)
NONE
Special Requisite(s)
NONE
Instructor(s)
Assoc. Prof. Esra Saatçı
Course Assistant(s)
NONE
Schedule
Tuesday 11:00-13:00 and Thursday 11:00-13:00
Office Hour(s)
Monday 13:00-15:00
Teaching Methods and Techniques
Lectures, practise
Principle Sources
Alberto Leon-Garcia (2008), “Probability, Statistics, and Random Processes for Electrical Engineering”, 3rd ed, Prentice Hall, 0-13-147122-8,
Other Sources
G. J. Dolecek (2013), “Random Signals and Processes Primer with MATLAB”, Springer, NewYork 2013 978-1-4614-2385-0
A. Papoulis and S.U. Pillai (2002), “Probability, Random Variables, and Stochastic Processes” , 4th ed, Mc-Graw Hill.
Sheldon Ross (2010), “A First Course in Probability”, Pearson, 0-13-607909-1.
R. D. Yates and D. J. Goodman (2005), “Probability and Stochastic Processes: A Friendly Introduction for Electrical and Computer Engineers”, 2nd ed, Wiley.
Course Schedules
Week
Contents
Learning Methods
1. Week
Probability Models in Engineering
Oral presentation, practise
2. Week
Basic Concepts of Probability -The sample Space, Events, Set operations, The Axioms of Probability
Oral presentation, practise
3. Week
Basic Concepts of Probability -Conditional Probability, Total Probability law, Bayes rule
Oral presentation, practise
4. Week
Basic Concepts of Probability -Independence of Events, Sequential Experiments
Oral presentation, practise
5. Week
Random Variables - Probability Mass Function
Oral presentation, practise
6. Week
Random Variables - Cumulative Distribution Function, Probability Density Function
Oral presentation, practise
7. Week
Midterm
Oral presentation, practise
8. Week
Random Variables - Conditional pmf, cdf, pdf
9. Week
Pairs of Random Variables
Oral presentation, practise
10. Week
Random Vectors
Oral presentation, practise
11. Week
Power Spectral Density
Oral presentation, practise
12. Week
Random Processes
Oral presentation, practise
13. Week
Multiple Random Processes
Oral presentation, practise
14. Week
Random Signal Response of LTI Systems
Oral presentation, practise
15. Week
16. Week
17. Week
Assessments
Evaluation tools
Quantity
Weight(%)
Midterm(s)
1
30
Homework / Term Projects / Presentations
1
20
Final Exam
1
50
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 modeling 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, analyze 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
Express basic principles of experiment, sample space, probability and probability axioms
LO-2
Discuss conditional probability, independence and Bayes rule
Understand the concept of random variables and the differences between discrete and continuous random variables
LO-5
Describe basic random variables (Bernoulli, Binomial, Uniform, Gaussian, Exponential)
LO-6
Calculate and use probability mass function, cumulative distribution function and probability density function for the basic random variables
LO-7
Calculate the expectation and variance of the basic random variables and functions of the basic random variables
LO-8
Describe the random processes and express the characterization of the output signal (mean, autocorrelation, power spectral density) if random process is the input to LTI systems.
