Course abstract

This course is aimed at the students who have already learnt about basic Probability distributions and Random variables, and are interested in learning the Mathematical formulation of Probability. We first discuss the modeling of sample space and events into a probability space and, Random variables as functions on such probability spaces. Then, using Measure Theoretic techniques, we discuss a theory of integration which unifies the formulas for the expectations of discrete and absolutely continuous Random variables. Towards the end, we look at various convergence theorems for expectations of Random variables and related inequalities. Students, who complete the course, should be able to apply these results towards advanced studies.