Randomness is a common thing that we came across in our daily life. Questions like how much traffic will be on my route today? how much I need to wait to catch a bus to my workplace? will I gain or lose money in stock market? may not have fixed answers as they are associated with events that are not in our control and could be treated as random. In this course, we will learn various probability techniques to model random events and study how to analyze their effect.
INTENDED AUDIENCE : All disciplines learnersPRE-REQUISITE : Introductory real analysisSUPPORT INDUSTRY : This is a basic course. All companies will recognize
Week 1: Introductions to events, probability, conditional probability, Bayes ruleWeek 2: Random Varaibles, Expectations, Variance, Various type of distributionsWeek 3: CDF and PDF of random variables. Conditional CDF and PDFsWeek 4: Jointly distributed random variables, covariance and independenceWeek 5: Transformation of random variables and their distributionsWeek 6: Introductions to Random processes. Stationary and ErgodicityWeek 7: Convergence of Sequence of RVs. (almost surely, in probability, in distributions).Week 8: Strong and weak law of large numbers, central limit theoremWeek 9: Discrete Markov chains. Stopping time and Strong Markov property Classification of Transient and Recurrent statesWeek 10: Counting Process, Poisson Processes and its applicationsWeek 11: Renewal Theory. Elementary and Renewal Reward Theorem andWeek 12: Introduction to Continuous Markov Chains