Integrated MSc-PhD Program

SYLLABUS

KSM1C04: Probability Theory

Probability Spaces, Axioms of probability and illustrations, Inclusion-exclusion principle and examples, Bonferroni inequalities, Independence and conditional probability, Bayes’ rule and applications, Discrete probability distributions and examples, Continuous probability distributions and examples, Joint distributions and change of variable formula, Expectation, moments and generating functions, Inequalities (Cauchy-Schwarz, Markov, Chebyshev, Chernoff), Conditional distributions and conditional expectation, Characteristic function and properties, Law of large numbers, Gaussian random variables and properties, Poisson limits, Central limit theorem, Simulation, Simple symmetric random walk.

Suggested texts:

1. 1. 1. 1. 1. 1. William Feller, An introduction to probability theory and its applications. Vol. I, Third edition, John Wiley & Sons, Inc., New York-London-Sydney, 1968.
               2. William Feller, An introduction to probability theory and its applications. Vol. II, Second edition, John Wiley & Sons, Inc., New York-London-Sydney, 1971.
               3. Sheldon Ross, A first course in probability, second ed., Macmillan Co., New York; Collier Macmillan Ltd., London, 1984.