

Course Information
Course Unit Title 
: 
Probability Theory and Stochastic Processes 
Course Unit Code 
: 
01EHB5214 
Type of Course Unit 
: 
Optional 
Level of Course Unit

: 
Second Cycle 
Year of Study

: 
Preb 
Semester

: 
255.Semester 
Number of ECTS Credits Allocated

: 
6,00 
Name of Lecturer(s) 
: 


Course Assistants 
: 

Learning Outcomes of The Course Unit 
: 
I. Random variables and related functions, II. Multivariate random variables, joint distributions and conditional distributions III. The expected value, moments and related concepts, IV. Special continuous and discrete random distributions and their properties, V. The concept of random processes and related definitions, VI. Stationary and independent processes and ergodicity, VII. Poisson, Wiener, Gauss, Markov processes and their properties

Mode of Delivery 
: 
FaceToFace

Prerequisities and Corequisities Courses 
: 
Unavailable

Recommended Optional Programme Components 
: 
Unavailable

Course Contents 
: 
Random variables, distribution function, probability mass and density functions; multivariate random variables, joint distributions, functions of random variables, conditional distributions; expected value, moments and related concepts; moment generating function, characteristic function; some special continuous and discrete distributions; random processes, basic definitions, stationary and independent processes, ergodicity; Poisson, Wiener, Gauss, Markov processes; the concepts of stochastic continuity, derivative, integral; the concept of power spectrum.

Languages of Instruction 
: 
TurkishEnglish

Course Goals 
: 
1.To improve the knowledge of students on probability theory, 2.To train students on random processes and related properties, 3.To provide a basis for the solution of the engineering problems involving stochastic structure, 4.To provide practice for developing critical thinking skills and solving open ended problems.

Course Aims 
: 
1.To improve the knowledge of students on probability theory, 2.To train students on random processes and related properties, 3.To provide a basis for the solution of the engineering problems involving stochastic structure, 4.To provide practice for developing critical thinking skills and solving open ended problems.

WorkPlacement 



Recommended or Required Reading
Textbook

: 
Bertsekas, Dimitri, and John Tsitsiklis. Introduction to Probability. 2nd ed. Athena Scientific, 2008. ISBN: 9781886529236.

Additional Resources

: 
1. Yates, R. D. ve Goodman, D. (2005). Probability and Stochastic Processes: A Friendly Introduction for Electrical and Computer Engineers. John Wiley and Sons. 2. Hsu, H. (2010). Probability, Random Variables, and Random Processes (Second Edition). McGraw Hill (Schaum's Outline Series). 3. LeonGarcia, A. (2008). Probability, Statistics, and Random Processes For Electrical Engineering (Third Edition). Prentice Hall. 4. Krishnan, V. (2006). Probability and Random Processes. WileyInterscienc. 5. Papoulis, A. (1991). Probability, Random Variables and Stochastic Processes (Third Edition). McGrawHill.

Material Sharing
Documents

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Assignments

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Exams

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Additional Material

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Planned Learning Activities and Teaching Methods
Lectures, Practical Courses, Presentation, Seminar, Project, Laboratory Applications (if necessary)


ECTS / Table Of Workload (Number of ECTS credits allocated)
Student workload surveys utilized to determine ECTS credits.

Activity

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Course Duration (Excluding Exam Week)

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Time Of Studying Out Of Class

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Presentation

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Workload Hour (30)

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Course's ECTS Credit

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Assessment Methods and Criteria
Studies During Halfterm

: 

Visa

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Quiz

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Homework

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Attendance

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Application

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Lab

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Project

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Workshop

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Field study

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TOTAL

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The ratio of the term to success

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The ratio of final to success

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TOTAL

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Weekly Detailed Course Content
Week

Topics

1

Introduction, random variables and classification



2

Distribution functions, probability mass and density functions



3

Multivariate random variables and joint distributions



4

Functions of random variables, conditional distributions



5

Expected value and moments, moment generating function, characteristic function, conditional expected value and moments,



6

Discrete probability distributions (Bernoulli, binom, negative binom, geometrik, hipergeometrik distributions)



7

Discrete probability distributions (Poisson distribution), continuous probability distributions (uniform,exponential,Gauss distributions)



8

Continuous probability distributions (Erlang, Cauchy,Gamma, Laplace ve diğerleri) , law of large numbers and central limit theorem



9

Random processes and related functions (Distribution, correlation, variance, covariance functions)



10

Stationary processes, independent processes, processes with independent stationary increments, ergodicity



11

Poisson process, Wiener process



12

Gauss process , Markov process



13

Concepts of stochastic continuity, derivative and integral



14

Concept of power spectrum



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