You can find all the course material here. For weekly slides, please see below
Topics: Probability Spaces, Permutations, Combinations and Conditioning
Reading: Chapter 1.4,1.5 SR - Models and SR Prob Sections 1.2-1.5, 3.1-3.5
Problem Set: Chapter 1 - Questions 19, 25, 40, 45, 48 - SR Models. Chapter 1 - Problems 10, 11, 12, 15, 29 - SR Prob.
Topics: Random variables, expected value, discrete models
Reading: SR Models Chapters 2.1-2.2, 2.4 and SR - Prob 4.1-4.7
Problem Set: SR Models Chapter 2 - Questions 4, 13, 16, 23, 27, 55(a), 55(b)
Topics: Continuous random variables: pdf, quantiles, continuous parametric models; transformations of a single random variable
Reading: SR Models Chapters 2.3-2.4, 5.2, SR Prob 5.1-5.7, Lecture slides for details on various models
Problem Set: SR Models Chapter 2 - Questions 30, 33, 34, 35, 37, 48, 53 and 74, and SR Prob. Theoretical Exercise from Chapter 4, Questions 2, 4, 14 19.
Topics: Moments of a random variable, Order statistics, generating functions, inequalities
Reading: SR Models 2.6, SR Prob 7.1-7.4
Problem Set: Additional Problem Set, SR Models Chapter 2, Questions 80, 81, 82, 93, 74, 76, 77
Topics: Multivariate distributions, change of variables formula, conditional densities
Reading: SR Models 2.5, SR Prob Chapter 6, Examples 1-7
Problem Set: SR Prob. Chapter 6, Problems 7-10, 14, 15, 20, 21, 22, 38, 40, 41, 43, 53, 54. SR Prob. Chapter 6, Theory Exercises 11, 12, 25
Topics: Multivariate Models: Multinomial, Diriechlet, Multivariate Gaussian and Elliptical distributions
Reading: Lecture Slides
Problem Set: Extra Problems for solution
Topics: Conditional Expectation, Projections and Martingales (time permitting)
Reading: SR Models 3.1-3.5, SR Prob 7.5, 7.6 and 7.9, DW Chapters 9 and 10. PB - Chapter 34-35 for a general treatment of conditional expectation and martingales
Problem Set: Solve homework questions, Problems 33, 43, 44, 46, 58, 72, 77, 78, 79 from SR Models, Chapter 3.
Topics: Convergence of Random variables, Law of large numbers, central limit theorem, confidence intervals
Reading: SR Models 2.7, Lecture slides. PB - Chapter 25-27 for a more general treatment
Problem Set: Solve homework questions
Topics: Introduction to Simulation: Input and Output analysis
Reading: PG-Chapter 2.2 and 2.3, GA-Chapter II lecture notes (Input analysis) and GA Chapter III for output analysis and confidence intervals.
Problem Set: Solve homework questions, play around with the R-code
Topics: An introduction to the statistics of decision making, an introduction to extremes
Reading: Lecture Slides for statistics of decision making and PE chapter 3.1-3.4 and lecture slides for introduction to extremes.
Problem Set: NA
Textbooks:
1) Sheldon Ross: A first course in probability - SR Prob
2) Sheldon Ross: Introduction to probability models 12th edition - SR Models
3) Paul Embrechts et al.: Modelling extremal events (only last class) - PE
Reference Books:
1) Patrick Billingsley - Probability and Measure (3rd edition) - PB
2) Paul Glasserman - Monte Carlo Methods in Financial Engineering - PG
3) Peter Glynn and Soren Asmussen - Stochastic Simulation - GA
4) William Feller - An introduction to probability (Vol. 1 and 2) - WF-I and WF-II
5) David Williams: Probability with Martingales (Chapters 9 and 10 only) - DW