Course Information

Course Name	Turkish	Olasılık&Rasgele Süreçler
	English	Probability Theory&Stochast.Pr
Course Code	KOM 505E	Credit	Lecture (hour/week)	Recitation (hour/week)	Laboratory (hour/week)
Semester	-	3	3	-	-
Course Language		English
Course Coordinator		Uluğ Bayazıt
Course Objectives		Review basic concepts on probability and random variables. Understand generalization of random variable concept to random sequences and random processes. Learn specific types of random sequences and random processes. Analyze random sequences and processes in transform domain. Analyze output of linear time invariant systems to random sequences and inputs in time and transform domains.
Course Description		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 cdf's and pdf's, 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.
Course Outcomes
Pre-requisite(s)
Required Facilities
Other
Textbook		Probability and Random Processes with Applications to Signal Processing, 3rd Edition H. Stark, J. W. WoodsPrentice Hall 2002.
Other References		1. INTUITIVE PROBABILITY AND RANDOM PROCESSES USING MATLAB, STEVEN M. KAY University of Rhode Island Springer 2006 2. Probability, Random Variables and Stochastic Processes, 4th edition, Athanasios Papoulis, Mc Graw Hill

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