EE 230	Probability and Random Processes	3-1-0-8
Syllabus: Introduction to probability: mathematical background - sets, set operations, sigma and Borel fields; Axiomatic definition of probability; properties of probability, conditional probability, independence, total probability, Bayes' rule; random variables: cumulative distribution function, probability mass function, probability density functions; Functions of a random variable; expectation - mean, variance and moments; characteristic and moment-generating functions; Jensen's inequality, Chebyshev, Markov and Chernoff bounds; special random variables-Bernoulli, binomial, Poisson, geometric, uniform, exponential, and Gaussian; Joint distribution and density functions; Bayes' rule for continuous and mixed random variables; joint moments, conditional expectation; Covariance and correlation- independent, uncorrelated and orthogonal random variables; function of two random variables; random vector- mean vector and covariance matrix; Multivariate Gaussian distribution; sequence of random variables: mean-square convergences, convergences in probability and in distribution, weak law of large numbers and central limit theorem; Elements of detection and estimation theory; hypothesis testing, minimum mean-square error (MMSE) and linear MMSE estimators; Random processes: discrete and continuous time processes; probabilistic structure of a random process; mean, autocorrelation and autocovariance functions; strict-sense stationary and wide-sense stationary (WSS) processes: autocorrelation and cross-correlation functions; Spectral representation of a real WSS process-power spectral density; examples of random processes: white noise and Poisson process. Texts 1. A. Leon-Garcia, Probability and Random Processes for Electrical Engineering, 3rd edition, Pearson, 2011. 2. H. Stark and J. W. Woods, Probability and Random Processes with Applications to Signal Processing,4^th edition, Pearson,2011. References 1. D. P. Bertsekas and J. N. Tsitsiklis, Introduction to Probability, 2nd edition. Athena Scientific, 2008. 2. K. L. Chung and F. AitSahlia, Elementary Probability Theory with Stochastic Processes and an Introduction to Mathematical Finance, 4th edition. Springer-Verlag, 2003. 3. A. Papoulis and S. U. Pillai, Probability Random Variables and Stochastic Processes, 4th edition. McGraw-Hill, 2002.