Introduction to Probability Theory and Stochastic Processes

This course explanations and expositions of probability and stochastic processes concepts which they need for their experiments and research. It also covers theoretical concepts of probability and stochastic processes pertaining to handling various stochastic modeling. This course provides random variable, distributions, moments, modes of convergences, classification and properties of stochastic processes, stationary processes, discrete and continuous time Markov chains and simple Markovian queueing models. INTENDED AUDIENCE : Under-graduate students of electrical engineering, computer engineering, mechanical engineering, civil engineering and mathematics and computing PREREQUISITES : A basic course on Calculus and Linear Algebra INDUSTRY SUPPORT : Fractal Analytics, Genpact, Goldman Sachs, FinMechanics, Deutsche Bank and other finance companies.

Week 1 : Basics of Probability Week 2 : Random Variable Week 3 : Moments and Inequalities Week 4 : Standard Distributions Week 5 : Higher Dimensional Distributions Week 6 : Functions of Several Random Variables Week 7 : Cross Moments Week 8 : Limiting Distributions Week 9 : Introduction to Stochastic Processes (SPs) Week 10 : Discrete-time Markov Chains (DTMCs) Week 11 : Continuous-time Markov Chains (CTMCs) Week 12 : Simple Markovian Queueing Models