Unit – I
Axioms of probability theory- Probability spaces - Joint and conditional probabilities- Bayes’ Theorem- Independent events.
Unit – II
Random Variable and random vectors -Distributions and densities. Independent random variables – Functions of one and two random variables.
Unit – III
Moments and characteristic functions- Inequalities of Chebyshev and Schwartz. Convergence concepts.
Unit – IV
Random processes- Stationarity and ergodicity - Strict sense and wide sense stationary processes - Covariance functions and their properties - Spectral representation - Wiener-Khinchine theorem.
Unit – V
Gaussian processes - Processes with independent increments - Poisson processes - Lowpass and Bandpass noise representations.