IE 621: Probability and Stochastic Models I

Prerequisite:  Instructor's permission

Contents

Models and techniques to deal with randomness that underlie many industrial and social systems. Emphasis on models, their properties and their applications (rather than proofs).

 

  • Introduction to Probability: conditional probability, independence, discrete random variables, expectation, moments, random vectors, joint and marginal distributions, continuous random variables, expectation, moments, joint and marginal densities, laws of large numbers.
  • Elementary stochastic processes: random walks, Markov chains: first step analysis, state classifications, invariant distributions, Finite state Markov chains, Chapman-Kolmogorov equations, limiting state probabilities, Stationary distributions. Memory-less property of exponential random variables and related models & examples, Poisson processes. Optional: basics of queuing theory, renewal theory, and applications.
References
  • D.P. Bertsekas and John N. Tsitsiklis, Introduction to Probability, 2002
  • Kai L. Chung, A Course in Probability Theory, 3rd Edition, Academic Press, 200.
  • William Feller, An Introduction to Probability Theory and Its Applications (2 Vols), Wiley, 2008.
  • Charles M. Grinstead and J. L. Snell, Introduction to Probability, AMS, 1997.
  • Jim Pitman, Probability, Springer, 1993
  • Jean Jacod and Philip Protter, Probability Essentials, Springer, 2004.
  • Sheldon Ross, Probability Models,10th Edition, Academic Press, 2010
  • Santosh S. Venkatesh, The Theory of Probability, Cambridge University Press, 2012.