
Instructor: Prof. Dr.Ing. Werner Henkel
Fundamental aspects of probability theory are covered, starting from basic concepts such as set theory, probability space, conditional probabilities, independence, the law of large numbers, to random variables, joint and marginal densities, general moments, transformations, the central limit theorem, and finally, to more advanced topics such as queuing theory, linear prediction, LMS and Kalman filters . Special attention is given to random processes and power spectral estimation.
Lecture at Old Dominion University (Spring 2015)

Text book:Papoulis, Pillai, Probability, Random Variables, and Stochastic Processes, Mc Graw Hill, 4th ed.
 The meaning of probability – Chapter 1
 Definitions of probability: classical, relative frequency, axiomatic
 Fundamental concepts in probability – Chapter 2
 Set theory
 The probability space
 Conditional probability and independence
 Repeated trials – Chapter 3 and Section 4
 Combined experiments / Bernoulli trials
 Asymptotic theorems
 Law of large numbers
 Rare events: Poisson theorem/random points
 The concept of a random variable – Chapter 4
 Distribution and density functions
 Conditional distributions and density functions
 Total probability and Bayes’ theorem
 Functions of one random variable – Chapter 5
 Functions of a random variable
 Mean, variance and general moments
 Characteristic functions
 Two random variables – Chapter 6
 Joint and marginal statistics
 Functions of two random variables
 Joint moments and characteristic functions
 Conditional distributions and expected values
 Sequences of random variables – Chapter 7
 Transformations
 Mean and covariance
 Conditional densities and characteristic functions
 The central limit theorem
 Random Processes – Chapter 9 and Section 12.1
 Statistics of random processes
 The independent increments property
 Stationary processes: strict sense and wide sense
 Systems with stochastic inputs
 The power density spectrum
 Ergodicity
 The meaning of probability – Chapter 1
