CS723 Probability and Stochastic Processes

CS723 Probability and Stochastic Processes

 COURSE CONTENT

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 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.

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