I am currently teaching a graduate course “ELE 525: Random Processes in Information Systems” at Princeton University on Mondays and Wednesdays in the Fall Semester 201314. I taught the same course in the Fall 201213. I post here the lecture slides, hoping that they will be useful to other instructors who will teach similar courses. The slides should be also useful to those who wish to study the subjects based on the textbook Probability, Random Processes and Statistical Analysis, by Hisashi Kobayashi, Brian L. Mark and William Turin (Cambridge University Press, 2012, 800 pages).
Lecture 1: Introduction: History and OverviewLecture 2: Probability and Random Variables
Lecture 3: More on Random Variables
Lecture 4: More on Random Variables and Functions of Random Variables
Lecture 5: Fundamental of Statistical Analysis, and Distributions Derived from Normal Distribution
Lecture 6: Rayleigh, Rice and Lognormal Distributions; Transform Methods and the Central Limit Theorem
Lecture 7: Generating Functions and the Laplace Transform
Lecture 8: Inequalities and Bounds; Modes of Convergence
Lecture 9: Modes of Convergencecont’d; Limit Theorems
Lecture 10: Limit Theoremscont’d; Introduction to Random Processes
Lecture 11: Introduction to Random Processescont’d
Lecture 12: Spectral Representations
Lecture 13: Generalized Fourier Series Expansion: The KarhuenenLoève Expansion
Lecture 14: Applications of the KL Expansion; and the Poisson Process
Lecture 15: DiscreteTime Markov Chains (DTMC)
Lecture 16: Classification of States in a DTMC; and SemiMarkov Processes
Lecture 17: ContinuousTime Markov Chains (CTMC)
Lecture 18: Random Walks and Brownian Motion
Lecture 19: Conditional Expectations, MMSE, and Regression Analysis
Lecture 20: Wiener Filter Theory
Lecture 21: Wiener Filter Theory Part 2
Lecture 22: MaximumLikelihood Estimation
Lecture 23: The ExpectationMaximization Algorithm; Hidden Markov Models (HMMs)
Lecture 24: Hidden Markov Models
Lecture 25: Hidden Markov Models (continued)
Homework #1 (Assigned on Wed. Sept. 25, 2013)
Homework #2 (Assigned on Wed. Oct. 2, 2013)
Homework #3 (Assigned on Fri. Oct. 11, 2013)
Midterm Examination (Mon. Oct 21, 2013)
Homework #4 (Unfinished problems in the midterm exam)
Homework #5 (Assigned on Tue. Nov. 5, 2013)
Homework #6 (Assigned on Mon. Nov. 13, 2013)
Homework #7 (Assigned on Tue. Nov. 26, 2013)
Self study exercise problems (Assigned on Dec. 16, 2013)
Homework #8 (Assigned on Wed. Dec. 20, 2013)
Final Examination (Mon. January 20, 2014)
Final Examination Solutions 

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