Probability

Course Code:

MATH 281

Course Period:

Autumn

Course Type:

Core

Credits:

3

Theoric:

2

Practice:

2

Laboratory Hour:

0

ECTS:

5

Prerequisite Courses:

Calculus II

Course Language:

English

Course Objectives:

The aim of this course is to familiarize students the fundamentals of probability theory using contemporary and practical examples. We provide necessary probability background for the students who want to work on communications, statistical signal processing related courses.

Course Content:

Basic concepts of probability, expectation and variance, distribution functions, Bayes' formula, marginal and conditional distributions, the distributions of sample statistics, law of large numbers and central limit theorem, hypothesis testing.

Course Methodology:

1: Lecture, 2: Problem Solving, 3: Simulation, 4: Seminar, 5: Interdisciplinary group working, 6: Laboratory, 7: Term research paper, 8: Guest Speaker, 9: Sample Project Review

Course Evaluation Methods:

A: Exam, B: Quiz, C: Experiment, D: Homework, E: Project

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Course Learning Outcomes

Learning Outcomes	Program Outcomes	Teaching Methods	Assessment Methods
1) Ability to question probabilistic thinking. Ability to define basic probabilistic definitions.	1,2,3	1,2	A,B
2) Ability to explain conditional probability. Koşullu olasılık kavramını açıklayabilme. Ability to formulate problems using the concept of random varibale.	1,2,3	1,2	A,B
3) Ability to differentiate between discrete and continous random variables.	1,2,3	1,2	A,B
4) Ability to relate the decision making problem with the probability density functions.	1,2,3	1,2	A,B
5) Ability to solve some basic problems in Electrical and Electronics Engineering using probability theory.	1,2,3,9	1,2,9	A,B

Course Flow

COURSE CONTENT
Week	Topics	Study Materials
1	Course overview, probabilistic models	Textbook
2	Counting	Textbook
3	Independence, Conditional probability, total probability theorem and Bayes' Rule	Textbook
4	Examples on total probability theorem and Bayes' Rule	Textbook
5	Discrete Random Variables, Bernoulli, Binomial, Geometric, Poisson random variables	Textbook
6	Examples on Discrete Random Variables, Midterm I	Textbook
7	Functions of random variables, Expectation, Mean and Variance	Textbook
8	Joint PMF's of multiple random variables, Conditioning and Conditional Expectation	Textbook
9	Continuous random variables and PDFs, Cumulative distribution functions	Textbook
10	Normal distribution and Bayesian Decision Rule	Textbook
11	Joint PDF's of Multiple random variables, Conditioning	Textbook
12	Midterm II	Textbook
13	Limit Theorems, Central limit theorem	Textbook
14	Covariance and Correlation	Textbook

Recommended Sources

Textbook	Introduction to Probability, 2nd edition, Dimitri Bertsekas and John N. Tsitsiklis, Athena Scientific, 2008
Additional Resources	A First Course in Probability, Sheldon Ross, Prentice Hall

Material Sharing

Documents	MIT Open Course Ware (OCW) - Probabilistic Systems Analysis and Applied Probability, http://ocw.mit.edu
Assignments
Exams	Solutions of Midterm exams.

Assessment

IN-TERM STUDIES	NUMBER	PERCENTAGE
Midterms	2	83
Quiz	2	17
Total		100
CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE		40
CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE		60
Total		100

Course’s Contribution to Program

COURSE'S CONTRIBUTION TO PROGRAM
No	Program Learning Outcomes	Contribution
No	Program Learning Outcomes	1	2	3	4	5
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.					X
2	Ability to identify, formulate, and solve Electrical and Electronics Engineering problems; ability to select and apply proper analysis and modeling methods for this purpose.					X
3	Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern design methods for this purpose.					X
4	Ability to devise, select, and use modern techniques and tools needed for engineering practice; ability to employ information technologies effectively.
5	Ability to design and conduct experiments, gather data, analyze and interpret results for investigating engineering problems
6	Ability to access information; For this purpose ability to perform database searching and conduct literature review.
7	Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually.
8	Ability to communicate effectively both orally and in writing; knowledge of a minimum of one foreign language.
9	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.			X
10	Awareness of professional and ethical responsibility.
11	Information about business life practices such as project management, risk management, and change management; awareness of entrepreneurship, innovation, and sustainable development.
12	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.

ECTS

Activities	Quantity	Duration (Hour)	Total Workload (Hour)
Course Duration	14	4	56
Hours for off-the-classroom study (Pre-study, practice)	14	4	56
Mid-terms	2	2	4
Quizes	2	0.5	1
Homework
Final examination	1	4	4
Total Work Load			121
Total Work Load / 25 (h)			4.84
ECTS Credit of the Course			5

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