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 12: Conditional Expectations - I: Inner Product Space of Random Variables, Definition/Properties of Conditional Expectations.

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.)