PROBABILITY THEORY and STOCHASTIC PROCESSES (KOM505E)

Instructor:

M. Ertuğrul Çelebi,  Professor

Room:  2420

Phone: (212) 285 3558

E-Mail:  mecelebi@itu.edu.tr

Url: http://web.itu.edu.tr/~mecelebi

Office Hours:  13:30-15:30 on Wednesday's or by appointment. 

Class room/hour: D1301, 13:40-16:30 Friday's.

Course Objective:

To obtain a solid knowledge of random variables, random sequences, and a basic knowledge of stochastic signals.

Content:

Random experiments, axioms of probability, techniques of counting, conditional probability, independence,

sequential experiments. Random variables, probability distributions, some important random variables: Bernoulli,

binomial, geometric, Poisson, uniform, exponential, Gaussian, gamma. Functions of random variables, expected

values, Chebyshev inequality, characteristic functions. Multiple random variables, joint cdfs and pdfs, independence,

conditional probability and conditional expectation, functions of  several random variables, expected values of

functions of vector random variables, multidimensional Gaussian random variables. Sums of random variables,

the law of large numbers, the central limit theorem. Random processes, distributions, mean, autocorrelation,

autocovariance, some important random processes: sum, binomial counting, random walk, Poisson, Wiener, Brownian

motion. Stationary random processes, derivatives and integrals of random processes, time averages of random processes

and ergodic theorems. Power spectral density, response of linear systems to random signals.  Markov Chains.

Grading Policy:

%20 Midterm I,  %30 Midterm II, %50 Final

Textbook:

Probability and Random Processes for Electrical Engineering, II nd. Ed., Alberto Leon-Garcia, Addison Wesley, 1994 or,

Probability, Statistics and Random Processes for Electrical Engineering, III rd. Ed., Alberto Leon-Garcia, Pren. Hall, 2009

Supplementary Books:

Probability, Random Variables and Stochastic Processes, IV th. Ed., A. Papoulis, U. Pillai, McGraw Hill, 2002

Probability and Random Processes with Applications to Signal Processing, III rd. Ed., J. Woods, H. Stark, Pren. Hall 2001

Intuitive Probability and Random Processes using MATLAB, Steven Kay, 2005, Springer

Tentative Time-Table:

Sept.20 Introduction,

Sept.27            Basic Concepts (Chap 2)

Oct. 04            Basic Concepts (Chap 2), Random Variables (Chap 3, pp. 84-93)

Oct. 11            Random Variables (Chap 3, pp. 94-120)

Oct. 18 Random Variables (Chap 3, pp. 120-137)

Oct. 25 No Class

Nov.01 Multiple Random Variables (Chap 4, pp. 191-214), MIDTERM I

Nov.15 Multiple Random Variables (Chap 4, pp. 215-242)

Nov.22            Sum of Random Variables (Chap 5, pp. 269-288)

Nov.29            Random Processes (Chap 6, pp. 329-345)

Dec.06            Random Processes (Chap 6, pp. 346-366)

Dec.13            Random Processes, (Chap 6),  MIDTERM II

Dec.20            Power Spectral Density, Linear System Output to Stationary Inputs (Chap.7)

Dec.27            Markov Chains  (Chap. 8)  

Solved Problems Ch.2

Solved Problems Ch.3

Solved Problems Ch.4

Solved Problems Ch.5

Solved Problems Ch.6

Solved Problems Ch.7

Markov Chains

Midterm 1 Grades

Midterm 2 Grades

Both sides of an A4 reminder (cheat) sheet is allowed
for the Final on conditions:
-It should be in your handwriting, no photocopy please.
-It should include no problem solutions, just formula reminder.
-They will be collected along with your answer sheets.

Final Exam will be held in classroom 5304