Probability
Lecture Slides
Sessions 1 and 2: Basics of Probability Theory
Problem Set: Chapter 1 - Questions 19, 25, 40, 45, 48 - SR Models
Reading: SR Models Chapter 1.
Sessions 3-7: Random variables
Problem Set: Chapter 2 SR Models Questions - 4, 7, 11, 16, 21, 33, 34, 35, 36, 55, 77, 78(a). Go through Section 2.6 for MGF computation. Chapter 3 SR Models Questions 53, 57.
Reading: SR Models Chapters 2.1-2.4, 2.6-2.7, 3.5 (for computing probabilities using conditioning)
Sessions 8-10: Multivariate distributions
Note: Mid-term syllabus only up to lecture 8
Problem Set: SR Models Chapter 2: Problems 68, 75 and SR Prob Chapter 6: Problems 6.8, 6.9, 6.20, 6.21, 6.48 Worked out examples 7(d), 7(e)
Reading: SR Models Chapter 2.5.
Sessions 11-13: Markov Chains/Poisson processes
Problem Set: SR Models Chapter 4: Problems 5, 28, 29, 49, solved examples 4.1-4.6, 4.8, 4.12 and SR Models Chapter 5: 44, 64, 39, 50
Reading: SR Models Chapter 4.1-4.2, 4.4 and SR Models 5.3.1-5.3.3, 5.4.1
Sessions 14-15: Conditional Expectation
Problem Set: SR Models Chapter 3: Problems 15, 20, 57, 58. SR-Prob Chapter 7: Problems 4, 40, Solved examples 5c ad 5d
Reading: SR Models Chapter 3.1-3.5.
Session 16-17: Limit Theorems
Problem Set: See slides
Reading: SR Prob Chapter 8.3-8.4.
Session 18: Monte Carlo Simulation
Session 19: Problem solving session
Session 20: Class presentation + Problem Solving Session - II
Assignments:
Assignment 2 (2 more small parts will be uploaded by the weekend)
Textbooks:
1) Introduction to Probability Models: Sheldon Ross (12th ed.)
2) A first course in Probability: Sheldon Ross (8th ed.)
References: As given in the slides/in class