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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 : Face-To-Face
Prerequisities and Co-requisities 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 : Turkish-English
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. Leon-Garcia, A. (2008). Probability, Statistics, and Random Processes For
Electrical Engineering (Third Edition). Prentice Hall.
4. Krishnan, V. (2006). Probability and Random Processes. Wiley-Interscienc.
5. Papoulis, A. (1991). Probability, Random Variables and Stochastic
Processes (Third Edition). McGraw-Hill.
Material Sharing
Documents :
Assignments :
Exams :
Additional Material :
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 :
Number Duration Total  
Course Duration (Excluding Exam Week) :
14 3 42  
Time Of Studying Out Of Class :
0 0 0  
Homeworks :
3 0 0  
Presentation :
0 0 0  
Project :
1 0 0  
Lab Study :
0 0 0  
Field Study :
0 0 0  
Visas :
1 0 0  
Finals :
1 0 0  
Workload Hour (30) :
30  
Total Work Charge / Hour :
42  
Course's ECTS Credit :
0      
Assessment Methods and Criteria
Studies During Halfterm :
Number Co-Effient
Visa :
1 50
Quiz :
0 0
Homework :
3 15
Attendance :
0 0
Application :
0 0
Lab :
0 0
Project :
1 35
Workshop :
0 0
Seminary :
0 0
Field study :
0 0
   
TOTAL :
100
The ratio of the term to success :
50
The ratio of final to success :
50
TOTAL :
100
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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