CS723 - Probability and Stochastic Processes
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Course Category: Computer Science/Information Technology
Course Level: Graduate
Credit Hours: 3
Pre-requisites: MTH101 STA301

Course Synopsis

This is a graduate level course. The course will start by presenting fundamental concepts of probability theory. It will then develop mathematically sound concepts of random variables and their processing through PDF and CDF.

Course Learning Outcomes

Upon successful completion of this course, students should be able to:
  • Feel comfortable about concepts and terminology of probability theory and its domains of application
  • Apply set-theoretic probabilistic modeling of un-predictable phenomena and academic and real-life problems
  • Solve simple problems related to random variables, their distribution functions, expected values, moments, and their conditional expectations
  • Work with jointly distributed pairs of random variables using their joint and marginal densities
  • Understand how sequence of random variables behave and converge to predictable behaviour

Course Contents

Introduction, Set Theory, Number Theory, Relations, Functions, Axioms of Probability Theory, Conditional Probability, Bayes’ Rule, Random Variables, Density Functions, Conditional Density Function, Uniform, Exponential & Gaussian Density Function, Expected Values, Moments, Joint Density, Marginal Density Function, Transformation of Random Variables, Conditional Expectations, Vectors and Sequence of Random Variables, Convergence of Sequences of Random Variables.

Course Related Links

Course Related valuable link provided by The University of Michigan
Useful link for course related material, taught by Robert Adler and Jonathan Taylor at Stanford University
Useful link for course related material, taught by Lubos Thoma at The University of Rhode Island
Useful link for course related material, taught by Prof. Cosma Shalizi at Carnegie Mellon University
Course Related valuable link provided by University of Cincinnati
Lecture Notes provided by Prof. Wlodzimierz Bryc at University of Cincinnati
Course Related valuable link
Course Instructor

Dr. Muhammad Akmal Butt
Ph.D, Georgia Institute of Technology, USA
Books

Probability, Random Variables and Stochastic Processes by A. Papoulis

Probability and Random Processes by Venkatarama Krishnan

Introduction to Stochastic Processes by G. Lawler