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

• A. Papoulis, S.U. Pillai: Probability, Random Variables and Stochastic Processes. Mcgraw-Hill. 4Th ed. 2002
• R.M. Gray, L.D. Davisson: An Introduction to Statistical Signal Processing. Cambridge University Press, Feb. 2010
• T. Kailath, A.H. Sayed, B. Hassibi: Linear Estimation. Prentice Hall, NJ, 2000
• H. Stark, J.W. Woods: Probability and Random Processes, with Applications to Signal Processing. Prentice-Hall, 3rd ed., 2001
• H.L. Van Trees: Detection, Estimation and Modulation Theory, Parts I and III, Wiley, 1968/2001
• S. Kay: Fundamentals of Statistical Signal Processing, Vol. I — Estimation Theory. Prentice Hall, 1993
• S. Kay: Fundamentals of Statistical Signal Processing, Vol. II — Detection Theory. Prentice Hall, 1998
• S. Kay: Intuitive Probability and Random Processes Using MATLAB. Springer, 2005

Additionally, the "Semesterapparat" to this Lecture may be of interest.

The course starts on Wed., Oct. 23, with a meeting about the organization.

Please send an EMail to Dr. Forutan (vahid.forutan(at)uni-ulm.de) if you want to attend the course.

The course is completely based on the textbook A. Papoulis, S.U. Pillai: Probability, Random Variables and Stochastic Processes. Mcgraw-Hill. 4th ed., 2002. Please borrow a copy of this book from the university library.