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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


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.
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