Prerequisites topics
IE1xx Probability & Statistics
Contents:
Models and techniques to deal with randomness that underlie many industrial and social systems. Emphasis on models, their properties and their applications.
- Elementary stochastic processes: random walks,
- Markov chains: first step analysis, state classifications, invariant distributions, Finite state Markov chains, Chapman-Kolmogorov equations, Recurrent Markov Chains, positive & null recurrence, limiting state probabilities, Stationary distributions.
- Gambler’s ruin, Random walk, Birth death chain
- Memory-less property of exponential random variables and related models & examples, Poisson processes.
- Queueing systems, Little law, PASTA
- Introduction to renewal processes, Machine repair problems, replacement problems.
References
- Sheldon Ross, Probability Models,10th Edition, Academic Press, 2010
- S. M. Ross, Stochastic processes, 2nd Edition, 1996, John Wiley, New York
- D.P. Bertsekas and John N. Tsitsiklis, Introduction to Probability, 2002
- R. W. Wolff, Stochastic modeling and the theory of queues, 1989, Prentice Hall Inc., Engle-woodCliffs
- Hoel, Port, Stone, Introduction to Stochastic Processes
- Jean Jacod and Philip Protter, Probability Essentials, Springer, 2004.
- James Norris, Markov Chains, CUP, 1998