SYLLABUSThe chapter and section references refer to the text, Probability and RandomProcesses for Electrical and Computer Engineers, by John A. Gubner1. Introduction: Probability Spaces• what do we mean by the word “probability”?• probability spaces (finite, countable and uncountable models)[sections 1.1-1.3]• elementary probability theory [sections 1.4, 1.7]• conditional probability and Bayes’s theorem [sections 1.5-1.6]2. Random Variables and Distribution• discrete and continuous random variables[sections 2.1-2.3, 4.1, 5.1-5.3]• Examples: binomial, Poisson, expo nential, Gaussian, . . .[sections 3.2, 4.1]• functions of random variables [section 5.4]• joint and marginal distributions [sections 7.1-7.2]• n-dimensional Gaussian distributions [sections 7.4- 7.5, 9.1-9 .2]3. Exp ectation• mean, variance and covariance [sections 2.4, 4.4]• independence and conditional distributions [sections 3.4, 7.3]• conditional expectation (a naive discussion) [sections 3 .5, 7.3]• least squares estimation for Gaussian random vectors[sections 9.4-9.5]• characteristic functions [sections 3.1, 4.3, 9.3]14. Limit theorems• laws of large numbers [sections 3.3]• central limit theorem [section 5.6]5. Stochastic Pro cesses - Foundations• finite-dimensional distributions and a discussion of Kolmogorov’stheorem on the existence of stochastic processes [sections 1 0.1-10.2, 11.4]• existence of continuous versions (quote only)6. Poisson process [section 11.1]• axiomatic definition• characterization as counting process with stationary and indepen-dent increments• int er-arrival times7. Gaussian processes with Wiener process as example• covariance function and spectral density [sections 10.3-10.4]• Wiener process (Brownian motion) [section 11.3]- equivalent characterizations and elementary properties• white noise (a naive introduction) [sections 10.5-10.6]8. An Brief Introduction to Markov processes• Chapman-Kolmogorov equations• Homogeneous Markov chains [sections 12.1-1 2.4] (only if time