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 Lisans Öğrencileri Lisansüstü Adayları

 Title: Probabılıty For Electrıcal Engıneers

 Credits: 4


Catalog Description: Probability for Electrical Engineers                                      (4+1+0) 4

Fundamentals of probability. Random variables, distribution and density functions and some specific functions. Operations on one random variable:  expectation, moments and transforms of random variables. Vector random variables, joint distribution and density functions. Statistical independence. Operations on multiple random variables. Some basic probabilistic processes. Random processes,  stationarity, independence and ergodicity, correlation function. Spectral characteristics of random processes. Linear systems with random inputs.

Coordinator: Ayşın Ertüzün, Professor of Electrical Engineering


Goals: The course is designed to familiarize students with the modeling and analysis of random phenomena.   Basic notions of probability theory as well as methods of modeling basic probabilistic and stochastic phenomena are introduced.  Students will couple engineering intuition with mathematical principles and develop insight into how to apply probability theory to practical situations.


Learning Objectives:


At the end of this course, students will be able to:

1.     Model simple probabilistic and stochastic phenomena mathematically.

2.     Calculate probabilities of events in a known event space, expected values and variances of random variables, output of linear systems driven by random processes bot in time and frequency domains


Textbook: R.D. Yates and D. J. Goodman, Probability and Stochastic Processes- A Friendly Introduction for Electrical and Computer Engineers, John Wiley & Sons, Inc., 2005 (2/e)

Reference Texts: A. Papoulis, Probability, Random Variables, and Stochastic Processes, Mc Graw Hill, 1984.


Prerequisites by Topic:

1.     Linear algebra

2.     Laplace Transform



1.     Historical background of probability
2.     Set theory, events, sample space, definition and axioms of probability (1 week)
3.     Discrete, continous and mixed random variables, probability mass funcitons, probability distribution functions, probability density functions, cumulative distribution functions, mean and variance (2 weeks)
4.     Families of continuous and discrete random variables
5.     Pairs of random variables and joint probability functions
6.     Random vectors and probability functions associated with them
7.     Applications of s and z transforms to probability distribution functions and probability density functions, sums of random variables (2 weeks)
8.     Gaussian probability density and the Central Limit Theorem (1.5 weeks)
9.     Stochastic processes, independent identically distributed random sequences, Poisson processes,Expected value and correlation, stationarity and wide sense stationary processes, ergodicity, Cross correlation, Gaussian processes
10.   Linear filtering of a continuous-time stochastic process and a random sequence, Power spectral density of a continuous-time stochastic process  and a random sequence, Cross spectral density, Frequency domain filter relationships
11.   Markov Chains- if time permits

Course Structure: The class meets for four lectures (two 50-minute sessions) and a problem sessions a week( a 50-minute session). Example problems are solved the problem sessions held by the teaching assistant. There are two closed-book in-class mid-term exams and a closed-book final exam. A formula sheet is given by the instructor.

Computer Resources: None.

Laboratory Resources: None.



1.     Two mid-term exams (30% each)

2.     A final exam (40%)


Outcome Coverage:


(a) Apply math, science and engineering knowledge. Different tools from mathematics (Boolean algebra, linear algebra, Laplace and z-transforms) are heavily drawn upon during lectures, homework sets and exams.

(e) Identify, formulate, and solve engineering problems. This course is about formulating mathematical models for life-like probabilistic phenomena and solving for some statistics of interest. 30% of the semester is dedicated to applying the theoretical knowledge to typical daily-life and engineering problems.


Prepared By: Ayşın Ertüzün



Boğaziçi Üniversitesi - Elektrik ve Elektronik Mühendisliği Bölümü

34342 - Bebek / İSTANBUL

Tel: +90 212 359 64 14
Fax: +90 212 287 24 65







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