# ADVANCED PROBABILITY AND RANDOM PROCESSES

This page has been produced for providing students with general informations and guidelines on the course of Advanced Probability and Stochastic Processes. If you have any questions after reading this page, send a mail to your professor.

SYLLABUS, print, and bring the hardcopy to the first class hour!!!

COURSE NAME

LECTURER

l  Professor Joong Kyu Kim(Rm#: 21225, Tel: 031-290-7122)

COURSE OBJECTIVE

l  To Learn the basics on probability, random variables, and stochastic processes in order to apply the concepts to a wide range of electrical, and electronis engineering fields.

COURSE DESCRIPTION

l  Basic concepts of probability theory. Random variables: discrete, continuous, and conditional probability distributions; averages and independence. Introduction to discrete and continuous random processes: wide sense stationarity, correlation and spectral density.

PREREQUISITE

l  Probability and Statistics

l  Probability and Random Processes

TEXTBOOK

l  Probability, Random Variables, and Random Signal Principles by P.Z.Peebles Jr.

REFERENCE

l  Elements of Engineering Probability & Statisticsby R.E.Ziemer

l  Probability and Random Processes by W.B.Davenport Jr.

l  Probability, Random Variables, and Stochastic Processes by A.Papoulis

l  Probability and Random Processes by A.Leon-Garcia

l  Probability and Stochastic Processes by Yates and Goodman

CLASSNOTE

l  For your convenience, the classnote in PS and PDF forms will be distributed in advance!!!

 Mid-term Exam 40% Final Exam 50% Attendance 10% Total 100%

Note:

l  All the exams are closed books, but you are allowed to bring one page of A4 size hand-written reference sheet to each examination

l  Homeworks will not be assigned during the course of the semester, but you are strongly encouraged to solve some of the problem sets in each chapter of the textbook as well as the references.

l  No grade change will be permitted at the end of the semester. (e.g. C or D to F)

TOPICS TO COVER

l  Probability

l  The Random Variable

l  Operations on One Random Variable - Expectation

l  Multiple Random Variables

l  Operations on Multiple Random Variables

l  Random Processes - Temporal Characteristics

l  Random Processes - Spectral Characteristic

l  Linear Systems with Random Inputs

l  Optimum Linear Systems

l  Some Practical Applications of the Theory

WEEKLY SCHEDULE

 Week No. Detailed Topics Week#1 Concept of probability: probability space, review of set theory, probability axioms Week#2 Conditional probability, total probability law, Bayes Theorem, independent events, theory of counting Week#3 Order space, Bernoulli trials, concepts of random variables, and probability distribution function Week#4 Continuity axiom, classification of random variables, probability density function Week#5 Gaussian and uniform random variables, conditional distribution and density functions, mathematical expectation Week#6 Characteristic function, moment generating function, nonlinear function of random variables Week#7 Extension of above concepts to two random variable cases, statistical independence, correlation --- Mid-term Examination --- Week#8 Function of multiple random variables, introduction to estimation theory: LMSE(Least Mean Squared Error) linear and nonlinear estimators Week#9 Introduction to random processes: basic concept, definition, classification, stationarity and independence, distribution and density functions Week#10 Ergodic Theorem, correlation functions, introduction to Gaussian random processes Week#11 Auto power spectral density of random processes: definition, properties, and relation to autocorrelation function Week#12 Cross power spectral density, concept of white and colored noises Week#13 Random signal response of linear systems: time domain and frequency domain characteristics, system evaluation Week#14 Bandpass, bandlimited, and narrowband random processes: definition and characteristics Week#15 Optimal linear systems: matched filter and Wiener filter --- Final Examination ---

Up