MTL106: Probability and Stochastic Processes
MTL106: Probability and Stochastic Processes
Axioms of probability, Probability space, Conditional probability, Independence, Bayes’ rule. Random variable, Some common discrete and continuous distributions. Distribution of Functions of Random Variable, Moments, Generating functions. Two and higher dimensional distributions. Functions of random variables, Conditional distributions, Covariance, Correlation coefficient, conditional expectation. Modes of convergences, Laws of large numbers, Central limit theorem.
Definition of Stochastic process, Classification and properties of stochastic processes. Simple Markovian stochastic processes, Gaussian processes, Stationary processes. Discrete and continuous time Markov chains, Classification of states, Limiting distribution, Birth and death process, Poisson process, Steady state and transient distributions, Simple Markovian queuing models (M/M/1, M/M/1/N, M/M/c/N, M/M/N/N).