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# Course Weekly Lecture Plan

 Week Topic 1 1 18/09 Basic probability Woods&Stark concepts, axioms and theorems. 1.1-1.7 Conditional, total probability. Bayes theorem. 2 25/09 Statistical Independence, combinatorics Woods&Stark Bernoulli trials, De-Moivre Laplace 1.8-1.11 and Poisson approximations to binomial. 2.1-2.4 Random variables, distribution and density functions. 3 09/10 Random variables, distribution Woods&Stark and density functions. Some important 2.1-2.5 random variables: Bernoulli, binomial, geometric, Poisson, uniform, exponential, Gaussian. 4 16/10 Functions of random variables, Woods&Stark expected values, moments, Chebyshev 3.1-3.2, 4.1,4.3,4.4,4.7 inequality, characteristic functions 5 23/10 Multiple random variables, joint distribution Woods&Stark and density functions. Conditional density and 2.6, 4.2, 4.3 distribution functions, conditional expectation, joint moments. 6 30/10 Midterm I (in class) 7 06/10 Functions of several random variables. Woods&Stark Discrete random vectors, 3.3-3.4 expectation vectors, covariance 5.1-5.4 matrices and their properties. 8 20/11 Decorrelation of random vectors Woods&Stark Multi-dimensional Gaussian law Chp. 5.4,5.6- 5.7 Characteristic functions of random vectors. 9 27/11 Random sequences: Probability space Woods&Stark and sequence, examples, countable Chp. 6.1 additivity, continuity of probability, statistical specification, distribution and density functions, discrete valued random sequence first and second order statistics and their properties. 10 04/12 Gaussian random sequence, random Woods&Stark walk, central limit theorem, independent Chp. 6.1-6.2 increments sequence, stationarity. Review of LTI systems. 11 11/12 Response of D.T. Linear and LTI systems to Woods&Stark random sequences. WSS random Chp. 6.3-6.5 sequences and power spectral density. Markov random sequences and Markov Chains. 12 18/12 Random Processes: Definition, statistical Woods&Stark specification, density and distribution Chp. 7.1-7.2 functions, first and second order statistics. Poisson counting process. 13 25/12 Midterm II (in class) 14 01/12 Wiener process, Markov process, Woods&Stark Markov chains, Markov property, Chp. 7.2 Chapman-Kolmogorov Equations. 15 self study C.T. linear systems with random inputs, Woods&Stark special classes of random processes, Chp. 7.3-7.5 stationarity, WSS processes, power spectral density. Stationary processes and LTI systems, Stationary sequences and LTI systems.