**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. |