Axiomatic Probability, conditional probability, sigma algebra, and Random variables, Random vectors and moments, Stochastic Processes and Examples, stochastic processes and linear systems, Gaussian random process, spectral analysis of stationary processes, Power Spectral Densities, Stationarity and Ergodicity. Information and Entropy: joint and conditional, Mutual information, KL divergence, Source Coding, Stationarity. Gaussian random process, Central limit theorem, Convergence of RV, Statistics and sampling; Estimation of distribution parameters from statistics; Hypothesis testing and significance; Bayesian updating of distributions; The Multivariate Normal Distribution, Estimation of the Mean Vector and the Covariance Matrix, Hypothesis testing: Neyman-Pearson theorem, likelihood ratio test and generalized likelihood ratio test, discrete and continuous time Markov chains, discrete time branching processes, birth and death processes, random walks, random samples, statistic, sampling distribution, chi-sq, t and F distributions, central limit theorem, statistical inference, point estimation, unbiasedness, MLEs, interval estimation of mean and variances, hypothesis testing, types of errors, one – sided, two – sided tests, tests concerning means and variances, goodness of fit tests