Random 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 answer as they are associated with random events. In this course we will learn various probability techniques to model a random events and study how to analyze them.
INTENDED AUDIENCE : All disciplines learners
PRE-REQUISITE : Introductory real analysis
SUPPORT INDUSTRY : This is a basic course. All companies will recognize
Week 1: Introductions to events, probability, conditional probability, Bayes rule
Week 2: Random Varaibles, Expectations, Variance, Various type of distributions
Week 3: CDF and PDF of random variables. Conditional CDF and PDFs
Week 4: Jointly distributed random variables, covariance and independence
Week 5: Transformation of random variables and their distributions
Week 6: Introductions to Random processes. Stationary and Ergodicity
Week 7: Convergence of Sequence of RVs. (almost surely, in probability, in distributions).
Week 8: Strong and weak law of large numbers, central limit theorem
Week 9: Discrete Markov chains. Stopping time and Strong Markov property Classification of Transient and Recurrent states
Week 10: Counting Process, Poisson Processes and its applications
Week 11: Renewal Theory. Elementary and Renewal Reward Theorem and
Week 12: Introduction to Continuous Markov Chains