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 : Moments of a distribution, Bivariate distribution, Covarience and Correlation
Week 6 : Generating Functions and their properties: Moment Generating Function Characteristic Functions and Probability Generating Function
Week 7 : Poisson Process, Conditional Expectations and Variance, Chebyshev's Inequality and Introduction to Bivariate Normal.
Week 8 : Functions of Random Variables, Introduction to t and F distribution.
Week 9 : Order Statistics
Week 10 : Limit Theorems: Mode of Convergence
Week 11 : Laws of Large numbers
Week 12 : Central Limit Theorems