Week 1 : Introduction, Sample Space, Probability Axioms, Theorems on Union and Intersections of events in a Sample Spaces. Bertrand’s Paradox.
Week 2 : Conditional Probability, Bayes Theorem, Probability on Finite Sample Spaces. Independence of Events..Week 3 : Introduction to Random variables – discrete & continuous Random variables Discrete random variables - Uniform, Bernoulli, Binomial, Geometric, Poisson Distributions, Hypergeometric, Negative Binomial
Week 4 : Continuous Random variables: Uniform, Normal, Exponential, Gamma, Cauchy, Beta1 and Beta2
Week 5 : Functions of Random Variables and their distributions, Introduction to T, Chi-Sq and F distributions.
Week 6 : Concept of multivariate Distribution Covariance, Correlation and Moments of a distribution.
Week 7 : Generating Functions and their properties: Moment Generating Function Characteristic Functions and Probability Generating Function
Week 8 : Bi-variate and Multivariate Random Variables
Week 9 : Order Statistics Continued Covariance between ith and jth order statistics
Week 10 : Limit Theorems: Mode of Convergence
Week 11 : Laws of Large numbers
Week 12 : Central Limit Theorems