
Course Category: 
Computer Science/Information Technology 
Course Level: 
Graduate 
Credit Hours: 
3 
Prerequisites: 
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 settheoretic probabilistic modeling of unpredictable phenomena and academic and reallife 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 


