National University of Sciences and Technology
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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 3-0
Pre-Requisutes 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
  • Leon-Garcia, Probability and Random Processes for Electrical Engineers (2nd edition), Addison-Wesley, 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