Prerequisite course : Familiarity with basic probability
Learning Objective
Modeling uncertainty is essential for effective decision making in many real life applications. Probability models provide the necessary framework to model uncertainty. The course aims to provide an exposure to basic concepts of probabilistic models and how it can be used to solve real problems.
Learning Outcomes
On successful completion of the course, the student will be able to
 state important definitions, and prove results in probability theory
 write codes for simulation studies
 formulate probabilistic models given real problems
 develop randomized algorithms
Course Content
Probability spaces, Axioms of Probability, Continuity of probability, Random variables, Common distributions, Distribution functions, Multiple random variables and Joint distributions, Functions of random variables, Moments, Conditional probability/expectation, Bayes rule, Sequences of random variables and convergence concepts, Laws of large numbers, Central limit theorem (3 weeks)
Stochastic process: Poisson process, Hazard functions, Random walk and Markov chain (2 weeks)
Estimators: maximum likelihood, maximum a posteriori Concentration inequalities: Markov, Chebyshev, Hoeffding, Chernoff inequalities (2 weeks)
Simulation: Inverse transformation method, Techniques for simulating continuous random variables, MCMC importance sampling, Rejection sampling, Gibbs sampling (3 weeks)
Models: Linear regression, hidden Markov models (2 weeks)
Randomized algorithms: Monte Carlo and Las Vegas methods, randomized quick sort, randomized algorithm for satisfiability (SAT). (2 weeks)
Text books

Ross, Sheldon M. Introduction to probability models. Academic press, 2014. ISBN13 :9780124079489

Ross, Sheldon M. A First Course in Probability. Pearson, Ninth edition, 2014. ISBN: 9789353065607.
References

Feller, Willliam. An Introduction to Probability Theory and its Applications. Vol.1. Wiley; 3rd Edition, 2008. ISBN13: 9780471257080

P.G.Hoel, S.C.Port and C.J.Stone, Introduction to Probability Theory. Houghtion Mifflin; 1 edition 1971. ISBN13: 9780395046364

Bertsekas, Dimitri P., and John N. Tsitsiklis. Introduction to Probability. Vol. 1. Athena Scientific, 2002. ISBN13: 9781886529236

Rohatgi, Vijay K., and AK Md Ehsanes Saleh. An Introduction to Probability and Statistics. John Wiley & Sons, 2015. ISBN13: 9781118799642
Past Offerings
 Offered in JulyDec, 2019 by Mrinal