Course Outlines and Prerequisites

<< Course Outlines and Prerequisites

MATH281 - Probability

  • Instructor:
  • COURSE INFORMATON

    Course Title

    Code

    Semester

    C +P + L  Hour

    Credits

    ECTS

    PROBABILITY

    MATH281

    4

    2+2+0

    3

    5

     

    Prerequisites

    MATH152 - Calculus II

     

    Language of Instruction

    English

    Course Level

    Undergraduate

    Course Type

    Core

    Course Coordinator

    Engin Masazade

    Instructors

    Engin Masazade

    Assistants

    Goals

    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.

    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.

     

    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

     

    Teaching Methods:

    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

    Assessment Methods:

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

     

     

    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 CATEGORY

    Expertise/Field Courses

     

    COURSE'S CONTRIBUTION TO PROGRAM

    No

    Program Learning Outcomes

    Contribution

    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 ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION

    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

     

  • Syllabus
  • Course Outline:

    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.