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EE 801 Stochastic Systems
Campus
PNEC
Programs
PG
Session
Fall Semester 2016
Course Title
Stochastic Systems
Course Code
EE 801
Credit Hours
30
PreRequisutes
Signal and Systems, Probability & Statistics (UG level)
Course Objectives
EE 801 covers fundamental analytical techniques that are used to model and process random variables and random processes in many areas of engineering, science, and other quantitative disciplines. The emphasis of this course is on the use of stochastic techniques in modern signal processing and systems modeling
Detail Content
Intro to Probability theory
Probability Spaces
Sample spaces
Event spaces
Probability Axioms
Mass analogy
Properties of prob. measures (example proofs)
Joint prob., conditional prob., independence
Set Theory Review
Counting Methods
Independent trials
Reliability problems
Random Variables
Discrete, continuous, mixed types
Creation of a new prob. space by a random variable
Common Distributions for random variables
Cumulative distribution function
Probability mass function (pmf) for a discrete random variable
Probability density function (pdf) for a continuous random variable
pdf for a mixed or discrete random variable
Moments of a random variable
Moment generating (MG) property & MG function
Functions of a Random Variable
Important Distribution Models for Discrete Random Variables
Important Distribution Models for Continuous Random Variables
Multiple Random Variables (Focus on two random variable)
Functions of Two (or More) Random Variables
Statistical independence of random variables
Correlation and covariance (Special moments, two random variables)
Sums of Random Variables
PDF of the sums of two random variables
Moment Generating functions of Sum of independent random variables
Central Limit Theorem
Stochastic Processes
Types of Stochastic processes
Random variables from random processes
IID random sequences
Poisson, Brownian and Gaussian Processes
Stationery processes
Wide Sense stationery processes
Cross correlation
Random Signal Processing
Linear Filtering of Continuous Time Stochastic process
Linear Filtering of a Random Sequence
Power Spectral Density of Continuous Time Stochastic processes
Power Spectral Density of Random Sequence
Cross Spectral density
Text/Ref Books
R D Yates and David J Goodman Probability and Stochastic processes (2nd edition) Wiley, 2005
LeonGarcia, Probability and Random Processes for Electrical Engineers (2nd edition), AddisonWesley, 1994
Time Schedule
Fall Semester 2014
Faculty/Resource Person
Dr Tariq Mairaj Khan
PhD Electrical Engineering (Michigan State University)
Discipline: Electrical Engineering
Specialization: Non Destructive testing