This class is a compressed course covering the following subjects:

• Probability for Electrical Engineering and Computer Science

  Review of basic probability and random variables; Axioms, basic laws, conditional probability, Bayes rule, independence; probability mass function, cumulative distribution function, probability density; function,joint, marginal and conditionaldistributions; mean, variance, covariance, correlation; Markov and Chebyshew inequalities; mean-square error estimation; hypothesis testing; Random vectors; Covariance matrix, Gaussian random vectors; laws of large numbers

• Random processes

  Discrete and continuous random processes, Wiener, Karhunen-Loeve, Neyman-Pearson; IID, Gauss-Markov, random walk; stationarity, autocorrelation function; power spectral density, White noise, bandlimited processes

• Detection and Estimation Theory

  Sufficient Statistics, Cramer-Rao Bound, Stein’s lemma, parameter estimation and Fisher-Information; hypothesis test; relative entropy; mutual information and MMSE; Filtering Noise