MA206

Probability theory and Random Processes (3 -0- 0) 3

Axioms of probability theory. Probability spaces. Joint and conditional probabilities- Bayes’ Theorem- Independent events.

Random variables and random vectors. Distributions and densities. Independent random variables – Functions of one and two random variables. 

Moments and characteristic functions. Inequalities of Chebyshev and Schwartz. Convergence concepts.

Random processes. Stationarity and ergodicity. Strict sense and wide sense stationary processes - Covariance functions and their properties. Spectral representation. Wiener-Khinchine theorem. 

Gaussian processes. Processes with independent increments. Poisson processes. Lowpass and Bandpass noise representations.

References:

Davenport, Probability and Random Processes for Scientist and Engineers, McGraw-Hill

Papoulis,A.,Probability, Random variables and Stochastic Processes, McGraw Hill.