Instructor:  Arvind Ayyer 
Office:  X15 (new wing) 
Office hours:  TBD 
Phone number:  (2293) 3215 
Email:  (First name) at iisc dot ac dot in 
Class Timings:  Mondays, Wednesdays and Fridays, 10:00 — 11:00 
Classroom:  LH4 (new wing, first floor) 
Textbook: 
Introduction to Probability Models (11th edition)
by Sheldon M. Ross Academic Press, 2014 ISBN13  9789351072249 Supplementary Texts: (a) Probability and random processes by Geoffrey R. Grimmett and David R. Stirzaker Oxford University Press, 2001 ISBN13  9780198572220 (b) Markov Chains and Mixing Times by David A. Levin, Yuval Peres and Elizabeth L. Wilmer Markov Chains and Mixing Times ISBN13  9780812847398 
TA: 

Tutorials:  Thursdays 9:30 — 10:00 
The date for the midterms and final will be announced later.
Here are the weights for the homework and exams.
All marks will be posted online
on Moodle.
week  date  sections  material covered  homework and other notes 
1  2/8  1.11.2  Basic set theory  Chap. 1: 1, 3, 4, 5, 6 
2  5/8  1.31.4  Probabilities  Chap. 1: 8, 11, 12, 13, 15, 19, 21 
7/8  1.51.6  Independence  Chap. 1: 36, 37, 40, 43, 45, 47  
8/8    Quiz 1 
  
9/8    Holiday 

3  12/8    Holiday 

14/8  2.12.2  Discrete random variables  Chap. 2: 1, 2, 4, 5, 9, 16, 17, 20, 30  
15/8    Holiday 
  
16/8  2.3  Continuous random variables  Chap. 2: 33, 34, 35, 36, 38  
4  19/8  2.4  Expectation  Chap. 2: 39, 40, 41, 47 
21/8  2.5  Functions of random variables  Chap. 2: 46, 47, 48  
22/8    Quiz 2 
  
23/8  2.5  Functions of random variables  
5  26/8  2.5  Joint random variables  Chap. 2: 49, 50, 53, 55 
28/8  2.5  Independence  Chap. 2: 56, 58, 59, 66  
29/8    Quiz 3 
  
30/8  2.5  Covariance  Chap 2: 54, 60, 62, 63  
6  2/9    Holiday 

4/9  2.5  Change of variables formulas  Chap 2: 68  
5/9    Quiz 4 
  
6/9  2.6  Moment generating functions  Chap 2: 67, 69, 70  
7  9/9  2.8  Limit theorems  Chap 2: 76, 78, 81, 83, 86 
11/9  2.9  Stochastic processes  none  
12/9    Quiz 5 
  
13/9  3.13.2  Conditional probability  Chap. 3: 1, 3, 5, 8  
8  16/9  Class cancelled 

18/9  3.33.4  Conditional expectation  Chap. 3: 11, 12, 15, 19, 21, 26, 30  
19/9    Quiz 6 
  
20/9  3.4  Conditional Variance formula  Chap. 3: 36, 38, 40, 49, 50  
9  23/9  No class (midterm week) 

25/9  Midsemester exam, 911am, LH4 

26/9    No class (midterm week) 
  
27/9  No class (midterm week) 

10  30/9  3.5  Probabilities by conditioning  Chap. 3: 53, 54, 56, 60 
2/10    Holiday 

3/10    Quiz 7 
  
4/10  4.1  Introduction to Markov chains  Chap. 4: 1, 3, 4, 6  
11  7/10  4.2  ChapmanKolmogorov equation  Chap. 4: 9, 12, 13 
9/10  4.3  Communication classes  Chap. 4: 15, 18(b), 21(a)  
10/10    Quiz 8 
  
11/10  4.3  Recurrence and transience  Chap. 4: 14, 16,  
12  14/10  4.4  Long run proportions  Chap. 4: 20, 21(b), 22, 24 
16/10  4.4  Stationary distribution  Chap. 4: 25, 26, 27, 28  
17/10    Quiz 9 
  
18/10  4.6  Aperiodicity  Chap. 4: 41, 42, 46, 47, 54, 59  
13  21/10  4.7  Branching processes  Chap. 4: 64, 66 
23/10  4.8  Reversible Markov chains  Chap. 4: 68, 70, 71, 73  
24/10    Quiz 10 
  
25/10  5.15.2  Exponential distribution  Chap. 5: 1, 3, 8, 10, 15  
14  28/10  5.3  Poisson process  Chap. 5: 32, 34, 37, 40 
30/10  5.3  Interarrival and waiting times  Chap. 5: 42, 44, 45, 57  
31/10    Quiz 11 
  
1/11    Holiday 

15  4/11  6.16.2  Continuoustime Markov chains  Chap 5: 59, 60, 64, 67
Chap 6: 1, 3, 4, 5 
6/11  6.3  Birthanddeath processes  Chap 6: 8, 9, 22, 25  
7/11    Quiz 12 
  
8/11  6.4  Kolmogorov's equations  Chap 6: 10, 11  
16  11/11  6.5  Limiting probabilities  Chap 6: 13, 16, 17, 19, 24 
13/11  6.6  Time reversibility  Chap 6: 29, 30, 32  
14/11    Quiz 13 
  
15/11  Class cancelled 

17  18/11  6.9  Matrix formulation  None! 
18  29/11    Final Exam 9:30am12:30pm 
Venue: LH 4 