EE 502 Stochastic Processes

Lecture Schedule

Tuesday 08:00 – 11:00 Semester Spring 2013

Credit Hours Three Pre-requisite Linear Algebra, Signals and

Systems and Probability

Instructor Muhammad Tahir Contact mtahir@uet.edu.pk

Office Office Hours Tuesday 11:00 – 12:00, Friday 10:00 – 11:00

Course Description

This is a pre-requisite for almost all graduate level courses in communications, signal processing, controls and networks. The course will assume an introductory knowledge of probability. We will first have a quick review of: axioms of probability, random variables, distributions, densities and functions of one random variable. Then functions of several random variables, moment generating functions, linear transformations and central limiting theorem will be discussed. After covering the topics related to random variables we will talk about stochastic processes, and their classifications. Furthermore we will talk about random walks, Markov chains, birth-death processes and their applications in queuing theory. The course also requires from each student critical reading and presentation of one relevant and recent research paper published in a reputed journal (e.g. IEEE, Elsevier, and Springer).

Expected Outcomes

Upon completion of this course, students will: Understand elements of probability theory and its application to various

problems in engineering. Become familiar with discrete and continuous probability distributions. Be able to transform, compute densities and expectations of random variables

and processes. Become familiar with random processes and the second moment theory. Be able to construct simple probabilistic models of queuing phenomenon

encountered in engineering.

Textbooks

REQUIRED: T1: Probability, Random Variables and Stochastic Processes by Athanasios Papoulis and S. U. Pillai, 4th Edition, McGraw Hill, 2002. T2: An Exploration of Random Processes for Engineers, by B. Hajek, 2011. Available at: http://www.ifp.illinois.edu/~hajek/Papers/randomprocDec11.pdf References: R1: D. P. Bertsekas, and J. N. Tsitsiklis. Introduction to Probability. Athena Scientific Press, 2nd edition, 2008. R2: Introduction to probability Models, S. M. Ross, 10th Ed., Academic Press, 2009.

Grading Policy

Assignments 10% Quizzes 10% Midterm 20% Final 50% Viva 10%

Lecture Plan

Weeks Topics Readings

1* Basic Concepts

Axiomatic Probability Theory, Discrete and Continuous Probability Space, Independent Events

Chapter 1 + 2 (T2)

1* Functions of One Random Variable

Single and Multiple Events, Distribution and Density Functions, Conditional density functions

Chapter 1 (T2), Chapter 5 (T1)

2* Functions of Two Random Variables,

One function of two random variables, Two functions of two random variables

Chapter 6 (T1)

1* Moment Generating Functions

First and Second order Moments Conditional Moments, Characteristic Functions

Chapter 7 (T1)

1*

Sequence of Random Variables Sum, Product, Random Vector, Correlation/Covariance Matrices, Convergence of sequence of random variables

Chapter 7 (T1)

2* Mean Square Error Estimation

Orthogonality principle, Linear estimators, Linear innovations sequences, Kalman filtering

Chapter 3 (T2), Chapter 9 (T1)

1 M I D T E R M

2* Stochastic Processes and Stationarity

Introduction to stochastic processes, Strict Sense Stationary, Wide Sense Stationary and Cyclo-stationary

Chapter 9 (T1)

1* Second Moment Theory

Autocorrelation, Linear Systems, Power Spectral Density, Convergence

Class Notes

2* Markov Chains

Introduction, Markov chains, State classifications, steady state behavior

Chapter 15 (T1), Chapter 4 (R2)

2* Birth-death Processes and Queuing Theory

Applications of Markov chains, Birth and Death processes, Birth-death process, Queuing theory

Chapter 6 + 8 (T2)

1* Introduction to Hidden Markov Models Hidden Markov models, forward-backward algorithm

Class notes

* - Tentative