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Eastern Mediterranean University
Faculty of Engineering
Department of Electrical and Electronic Engineering
EE571 – Probability Theory and Stochastic Processes
Year and Semester
Credit Hour
Pre/Co-requisite(s)
Academic Term
: 5, Fall
: (3, 0) 3
: Math 322 Probability and Statistical Methods
: Fall Semester 2006-2007
Catalog Description:
Probability theory. Random variables, distribution and density functions, expectation, moments, characteristic functions,
functions of random variables, sequences, convergence concepts. Weak and Strong Law of Large Numbers, the Central Limit
Theorem. Stochastic processes, mean, autocorrelation, autocovariance, cross-correlation, cross-covariance. Orthogonal and
independent processes. Stochastic differential equations. Ergodicity. Power spectral density. Gaussian, Poisson, Markov
processes.
Prerequisite:
Math322 Probability and Statistical Methods (Introduction to probability and statistics. Operations on sets. Counting
problems. Conditional probability and total probability formula, Bayes' theorem. Introduction to random variables, density and
distribution functions. Expectation, variance and covariance. Basic distributions. Joint density and distribution function.
Descriptive statistics. Estimation of parameters, maximum likelihood estimator. Hypothesis testing.)
Instructor:
Assoc. Prof. Dr. Huseyin Bilgekul
Office Hours: Monday 10:30–12:20, Wednesday 10:30–10:20 (Otherwise: Anytime I am available in my office)
Office Telephone: 630-1333
E-mail: [email protected]
Course Web Page: http://www.ee.emu.edu.tr/ee571
Textbook:
K.S. Shanmugan, A. M. Breipoh, Random signals : Detection, Estimation and Data Analysis l, John Wiley, 1988.
References:
1. A. Papoulis and S. U. Pillai, Probability, Random Variables and Stochastic Processes, Fourth Edition,
McGraw-Hill, Inc, USA, 2002.
2. A. L. Garcia, Probabilty and Random Processes for Electrical Engineering, Second Edition, Addison Wesley,
USA, 1994.
3. P. Z. Peebles, Probability, Random Variables and Random Signal Principles (Fourth Edition), McGraw Hill,
USA, 2001.
Course Objectives :
The primary goal of this course is to convey the main concepts and techniques of probability theory and stochastic
processes. At the end of the course the student will have




Acquired the fundamental concepts of probability theory ( random experiments, outcomes, events, independence,
correlation, conditional probability, distribution and density, expectations ...)
Learn some important results on probability : Total probability theorem, Bayes' theorem, transformations on random
variables, weak and strong laws of large numbers, the central limit theorem ...
Acquired fundamental concepts of stochastic processes : distributions, autocorrelation, autocovariance, stationarity,
power spectra, ergodicity ...
Learn some of the most important stochastic processes used in practice to model random phenomena : Gaussian,
Poisson, Markov processes ...
Course Web Page: http://www.ee.emu.edu.tr/ee571
COURSE OUTLINE AND ORGANIZATION
Week
No.
Hours
Description
1) Review of Probability Theory:
Set definitions, useful laws of probability, joint, marginal and conditional probabilities. (Chp. 2).
2) Random Variables and Transformations:
Distribution functions, expectations, probability density functions. Multivariate distributions, random
vectors, properties of multivariate Gaussian distribution. Transformation of random variables. (Chp.
2). (Chp. 2).
3) Bounds and Approximations:
Chernoff bound, Thebycheff inequality, approximating probability density functions. Series
approximation of pdf’s. (Chp. 2).
4) Sequences of Random Variables and Convergence:
Sequences of random variables and convergence. Convergence everywhere and almost everywhere,
Central Limit Theorem, Convergence in mean square. (Chp. 2).
5) Random Processes:
The concept and classification of random processes and methods of description. (Chp. 3).
6) Special Classes of Random Processes:
Random walk and Wiener processes, Poisson processes. Stationarity and different forms of
stationarity. (Chp. 3).
7) Autocorrelation and Power Spectral Density of WSS Random Processes:
Auto and cross correlation functions, PSD, PSD function of random sequences. (Chp. 3).
8) Time Averaging and Ergodicity: Continuity, differentiation and integration of random processes.
Time averages and ergodicity. (Chp. 3).
9) Response of Linear Systems to Random Inputs:
Response of LLTIC discrete time systems. Response of LLTIC continous time systems. (Chp. 4).
10) Special Classes of Random Processes:
Discrete linear models, Markov sequences and processes, point processes, Gaussian processes. (Chp.
5).
FINAL EXAMS
Computer Simulation Projects: Computer simulation projects will be given as assignments to be deleivered.
GRADING POLICY
Midterm I
Midterm II
Final Examination
Assignments
25%
25%
30%
20%
GRADING RULES:
The NG grade will be applicable to those students having an attendance of less than 60%. Students with such a low
attendance are not allowed to take make-up exams for their missing exams.
Course Web Page: http://www.ee.emu.edu.tr/ee571