Lecture Slides
Lecture 1: A review of first principles
Lecture 2: Combinatorial Probability
Problem Set: Chapter 1 - Questions 19, 25, 40, 45, 50 - SR Models
Lecture 3: Random variables - I: Definitions and discrete distributions
Problem Set: Chapter 2 Questions - 15, 17, 23, 27, 46, 55, 77 - SR Models
Lecture 4: Random variables - II: Continuous distributions in one dimension
Problem Set: Chapter 2 Questions - 34, 48, 49, 53, 74 - SR Models
Lectures 5-6: Random variables - III: Multivariate Random Variables
Problem Set: Chapter 2 Questions - 68, 71, Worked out examples from Section 2.5 - SR Models
Lecture 7: Moment Generating Function, inequalities, risk measures
Problem Set: Chapter 8: Questions 8.19, 8.21 (Main Problem set), 8.10-8.13 (Theoretical Exercises) and 8.13 (Self test problems) - SR Prob
Lecture 8: Convergence of Random Variables - I: Modes of Convergence
Problem Set: Chapter 8: Questions 8.13 (Theoretical Exercises) - SR Prob
Lectures 9-10: Convergence of Random Variables - II: Characterisations, Central Limit Theorem, Statistics
Problem Set: Chapter 2 SR Models: Questions - 68, 71
Lecture 11: Convergence of Random Variables - III: Modelling Extremes
Lecture 13-14: Conditional Expectations - II: Applications, Martingales
Problem set: Chapter 3 SR Models: Questions 17, 18, 33, 42, 43, 53, 67, 77, 93 and all other star marked problems from SR-Models, in class examples
Lecture 15-17: Markov Chains and Poisson Processes
Problem Set:
(i) Markov Chains: Chapter 4 SR Models: Questions 6, 9, 13 14, 16, 20, 21, 27, 29, 37, 49, 55
(ii) Poisson Processes: Problems as indicated at the end of the slides
Lecture 18-19: Monte Carlo Simulation
Problem Set: Review in class examples
SR Models - Sheldon Ross: Introduction to Probability Models (12th ed.)
SR Models - Sheldon Ross: A first course in probability (8th ed.)