Syllabus

Introduction to Probability: Sets and set operations, probability space, conditional probability and Bayes theorem, combinatorial probability and sampling models.

Random Variables: Discrete random variables, probability mass function, probability distribution function, example random variables and distributions continuous random variables, probability density function, probability distribution function, example distributions Joint distributions, functions of one and two random variables, moments of random variables conditional distribution, densities and moments, characteristic functions, Markov, Cheby-shev and Chernoff bounds, cetection and estimation.

Sequence of Random Variables and Convergence: Random sequences, Almost sure (a.s.) convergence and strong law of large numbers convergence in mean square sense with examples from parameter estimation convergence in probability with examples convergence in distribution central limit theorem.

Random Processes: Random processes, stationary processes, mean and covariance functions, ergodicity, linear filtering of random processes, power spectral density, examples of random processes: white noise process and white noise sequence, Gaussian process, Poisson process, Markov process.

To introduce student to the fundamentals and principles of random signals and stochastic processes.

To provide students the tools needed to analyse systems involving random signals.

To improve their skills in analyzing random phenomena which occur in Electrical Engineering application.

At the end of the course, students will be able to
1. Understand the axiomatic formulation of modern Probability Theory and think of random variables as an intrinsic need for the analysis of random phenomena.
2. Characterize probability models and function of random variables based on single & multiples random variables.
3. Evaluate and apply moments & characteristic functions and understand the concept of inequalities and probabilistic limits.
4. Understand the concept of random processes and determine covariance and spectral density of stationary random processes.
5. Demonstrate the specific applications to Poisson and Gaussian processes and representation of low pass and band pass noise models.

A Papoulis and S. Unnikrishna Pillai, Probability, Random Variables and Stochas- tic Processes, McGraw Hill

H. Stark and J. W. Woods, Probability and Random Processes with applications to Signal Processing, Pearson Education

S. Ross, Stochastic Processes, Wiley

W. Feller, An Introduction to Probability Theory, Wiley

Elsevier Journal on "Stochastic Processes & their Applications"

IEEE Transaction on Information Theory