Department of Biomedical Engineering

MATH 240 | Course Introduction and Application Information

Course Name

Probability for Engineers

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
MATH 240	SPRING	3	0	3	6

Prerequisites	MATH 154 To get a grade of at least FD
Course Language	English
Course Type	Required (Core Course)
Course Level	First Cycle
Mode of Delivery	face to face
Teaching Methods and Techniques of the Course	Lecture / Presentation
National Occupational Classification Code	-
Course Coordinator	Doç. Dr. Cemal Murat Özkut
Course Lecturer(s)	assistant_lecturer Gözde Navruz Uysal Doç. Dr. Cemal Murat Özkut
Assistant(s)	-

Course Objectives

This course aims to introduce students the theory of probability and its applications to engineering problems.

Learning Outcomes

The students who succeeded in this course;

Name	Description	PC Sub	* Contribution Level
Name	Description	PC Sub	1	2	3	4	5
LO1	Use fundamental concepts such as sample space, events and counting techniques. explain concepts of probability.	1.1					X
LO2	Use conditional probability, the total probability rule and Bayes' theorem. compute discrete and continuous random variables.	1.1					X
LO3	İnvestigate the advantages of joint probability distributions.	1.1					X
LO4	Apply discrete and continuous distributions.	1.1					X
LO5	Examine the relationship between two random variables.	1.1					X
LO6	Find mean and variance of random variables.	1.1					X

Course Description

In this course some important theorems about probability are investigated. In addition, applications of random variables and their probability distributions are discussed.

Related Sustainable Development Goals

Course Category	Core Courses
	Major Area Courses	X
	Supportive Courses
	Media and Managment Skills Courses
	Transferable Skill Courses

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week	Subjects	Required Materials	Learning Outcome
1	Sample space and events	Douglas C. Montgomery, Geroge C. Runger, “Probability”, Chap. 2 Applied Statistics and Probability for Engineers, 7th Edition (United States of America: Wiley, 2018), 18-23.	-
2	Events and counting sample points	Douglas C. Montgomery, Geroge C. Runger, “Probability”, Chap. 2 Applied Statistics and Probability for Engineers, 7th Edition (United States of America: Wiley, 2018), 21-26.	-
3	Counting sample points, probability of an event and additive rules	Douglas C. Montgomery, Geroge C. Runger, “Probability”, Chap. 2 Applied Statistics and Probability for Engineers, 7th Edition (United States of America: Wiley, 2018), 23-31.	-
4	Additive rules, conditional probability of an event	Douglas C. Montgomery, Geroge C. Runger, “Probability”, Chap. 2 Applied Statistics and Probability for Engineers, 7th Edition (United States of America: Wiley, 2018), 29-38.	-
5	Bayes’ rule	Douglas C. Montgomery, Geroge C. Runger, “Probability”, Chap. 2 Applied Statistics and Probability for Engineers, 7th Edition (United States of America: Wiley, 2018), 39-40.	-
6	Concept of random variable and discrete random variable	Douglas C. Montgomery, Geroge C. Runger, “Probability”, Chap. 2 and “Discrete random variable and Probability Distributions”, Chap. 3 Applied Statistics and Probability for Engineers, 7th Edition (United States of America: Wiley, 2018), 40-43.	-
7	Discrete probability distributions, expected value and variance of discrete random variable	Douglas C. Montgomery, Geroge C. Runger, “Discrete random variable and Probability Distributions”, Chap. 3 Applied Statistics and Probability for Engineers, 7th Edition (United States of America: Wiley, 2018), 43-49.	-
8	Uniform, Binomial, Negative Binomial, Hypergeometric, Poisson distributions (vaccine efficacy, epidemics, communicable diseases, traffic accidents, environmental pollution)	Douglas C. Montgomery, Geroge C. Runger, “Discrete random variable and Probability Distributions”, Chap. 3 Applied Statistics and Probability for Engineers, 7th Edition (United States of America: Wiley, 2018), 49-65.	-
9	Midterm Exam		-
10	Continuous probability distributions, expected value and variance of continuous random variable	Douglas C. Montgomery, Geroge C. Runger, “Continuous random variable and Probability Distributions”, Chap. 4 Applied Statistics and Probability for Engineers, 7th Edition (United States of America: Wiley, 2018), 67-72.	-
11	Uniform, Normal, areas under the normal curve, applications of the normal dist. and exponential distribution	Douglas C. Montgomery, Geroge C. Runger, “Continuous random variable and Probability Distributions”, Chap. 4 Applied Statistics and Probability for Engineers, 7th Edition (United States of America: Wiley, 2018), 73-86.	-
12	Joint probability distributions	Douglas C. Montgomery, Geroge C. Runger, “Joint Probability Distributions”, Chap. 5 Applied Statistics and Probability for Engineers, 7th Edition (United States of America: Wiley, 2018), 100-113.	-
13	Joint probability distributions, variance and covariance	Douglas C. Montgomery, Geroge C. Runger, “Joint Probability Distributions”, Chap. 5 Applied Statistics and Probability for Engineers, 7th Edition (United States of America: Wiley, 2018), 100-113.	-
14	Multinomial distributions, linear functions of random variables, moment-generating functions	Douglas C. Montgomery, Geroge C. Runger, “Joint Probability Distributions”, Chap. 5 Applied Statistics and Probability for Engineers, 7th Edition (United States of America: Wiley, 2018), 113-114, 117-120, 121-124.	-
16	Semester review		-
17	Final Exam		-

Course Notes/Textbooks	Douglas C. Montgomery Geroge C. Runger Applied Statistics and Probability for Engineers 7th Ed. (United States of America: Wiley 2018). ISBN: 978-1-119-40036-3
Suggested Readings/Materials	Ronald E. Walpole Raymond H. Myers Sharon L. Myers Keying Ye Probability and Statistics for Engineers and Scientists 9th Edition (United States of America: Pearson 2017). ISBN-13: 978-0321629111 William Navidi Statistics for Engineers and Scientists 5th Ed. (United States of America: Mc-Graw Hill 2019) ISBN-13: 978-1260547887

EVALUATION SYSTEM

Semester Activities	Number	Weighting	LO1	LO2	LO3	LO4	LO5	LO6
Final Exam	1	50	X	X	X	X	X	X
Midterm	1	40	X	X	X	X	X	X
Quizzes / Studio Critiques	1	10	X	X	X	X	X	X
Total	3	100

ECTS / WORKLOAD TABLE

Semester Activities	Number	Duration (Hours)	Workload
Participation	-	-	-
Theoretical Course Hours	16	3	48
Laboratory / Application Hours	-	-	-
Study Hours Out of Class	14	3	42
Field Work	-	-	-
Quizzes / Studio Critiques	2	10	20
Portfolio	-	-	-
Homework / Assignments	-	-	-
Presentation / Jury	-	-	-
Project	-	-	-
Seminar / Workshop	-	-	-
Oral Exams	-	-	-
Midterms	1	30	30
Final Exam	1	40	40
		Total	180

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#	PC Sub	Program Competencies/Outcomes	* Contribution Level
#	PC Sub	Program Competencies/Outcomes	1	2	3	4	5
1	Engineering Knowledge: Knowledge of mathematics, science, basic engineering, computation, and related engineering discipline-specific topics; the ability to apply this knowledge to solve complex engineering problems.
	1	Mathematics					LO1 LO2 LO3 LO4 LO5 LO6
	2	Science
	3	Basic Engineering
	4	Computation
	5	Related engineering discipline-specific topics
	6	The ability to apply this knowledge to solve complex engineering problems
2	Problem Analysis: Ability to identify, formulate and analyze complex engineering problems using basic knowledge of science, mathematics and engineering, and considering the UN Sustainable Development Goals relevant to the problem being addressed.
3	Engineering Design: The ability to devise creative solutions to complex engineering problems; the ability to design complex systems, processes, devices or products to meet current and future needs, considering realistic constraints and conditions.
	1	Ability to design creative solutions to complex engineering problems
	2	Ability to design complex systems, processes, devices or products to meet current and future needs, considering realistic constraints and conditions
4	Use of Techniques and Tools: Ability to select and use appropriate techniques, resources, and modern engineering and computing tools, including estimation and modeling, for the analysis and solution of complex engineering problems, while recognizing their limitations.
5	Research and Investigation: Ability to use research methods to investigate complex engineering problems, including literature research, designing and conducting experiments, collecting data, and analyzing and interpreting results.
	1	Literature research for the study of complex engineering problems
	2	Designing experiments
	3	Ability to use research methods, including conducting experiments, collecting data. analyzing and interpreting results
6	Global Impact of Engineering Practices: Knowledge of the impacts of engineering practices on society, health and safety, economy, sustainability, and the environment, within the context of the UN Sustainable Development Goals; awareness of the legal implications of engineering solutions.
	1	Knowledge of the impacts of engineering practices on society, health and safety, economy, sustainability, and the environment, within the context of the UN Sustainable Development Goals
	2	Awareness of the legal implications of engineering solutions
7	Ethical Behavior: Acting in accordance with the principles of the engineering profession, knowledge about ethical responsibility; awareness of being impartial, without discrimination, and being inclusive of diversity.
	1	Acting in accordance with the principles of the engineering profession, knowledge about ethical responsibility ethical responsibility
	2	Awareness of being impartial and inclusive of diversity, without discriminating on any subject
8	Individual and Teamwork: Ability to work effectively, individually and as a team member or leader on interdisciplinary and multidisciplinary teams (face-to-face, remote or hybrid).
	1	Ability to work individually and within the discipline
	2	Ability to work effectively as a team member or leader in multidisciplinary teams (face-to-face, remote or hybrid)
9	Verbal and Written Communication: Taking into account the various differences of the target audience (such as education, language, profession) on technical issues.
	1	Ability to communicate verbally
	2	Ability to communicate effectively in writing
10	Project Management: Knowledge of business practices such as project management and economic feasibility analysis; awareness of entrepreneurship and innovation.
	1	Knowledge of business practices such as project management and economic feasibility analysis
	2	Awareness of entrepreneurship and innovation
11	Lifelong Learning: Lifelong learning skills that include being able to learn independently and continuously, adapting to new and developing technologies, and thinking questioningly about technological changes.