Hisashi Kobayashi's Blog

Sherman Fairchild University Professor Emeritus of Electrical Engineering and Computer Science, Princeton University

Lecture Slides of Probability, Random Processes and Statistical Analysis

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 2013-14. I taught the same course in the Fall 2012-13. 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 Convergence-cont’d; Limit Theorems

Lecture 10: Limit Theorems-cont’d; Introduction to Random Processes

Lecture 11: Introduction to Random Processes-cont’d

Lecture 12: Spectral Representations

Lecture 13: Generalized Fourier Series Expansion: The Karhuenen-Loève Expansion

Lecture 14: Applications of the K-L Expansion; and the Poisson Process

Lecture 15: Discrete-Time Markov Chains (DTMC)

Lecture 16: Classification of States in a DTMC; and Semi-Markov Processes

Lecture 17: Continuous-Time 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: Maximum-Likelihood Estimation

Lecture 23: The Expectation-Maximization 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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