MA 261: Probability Models

Instructor: Arvind Ayyer
Office: X-15 (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: LH-4 (new wing, first floor)
Textbook: Introduction to Probability Models (11th edition)
by Sheldon M. Ross
Academic Press, 2014
ISBN-13 - 978-9351072249

Supplementary Texts:
(a) Probability and random processes
by Geoffrey R. Grimmett and David R. Stirzaker
Oxford University Press, 2001
ISBN-13 - 978-0198572220

(b) Markov Chains and Mixing Times
by David A. Levin, Yuval Peres and Elizabeth L. Wilmer
Markov Chains and Mixing Times
ISBN-13 - 978-0812847398
TA:
  • Dipankar Roy (dipankarroy at iisc dot ac dot in)
Tutorials: Thursdays 9:30 — 10:00

Course Description

Sample spaces, events, probability, discrete and continuous random variables, Conditioning and independence,
Bayes' formula, moments and moment generating function, characteristic function, laws of large numbers,
central limit theorem, Markov chains, Poisson processes.

Prerequisites

Basic linear algebra and some exposure to proofs and abstract mathematics.

Exams

All exams will be closed book, closed notes, and
no calculators or electronic devices are allowed (no cell/smart phones).
No communication among the students will be tolerated.
There will be no make up exams.

The date for the midterms and final will be announced later.


Grading

Here are the weights for the homework and exams.
All marks will be posted online on Moodle.


Tentative Class Plan

Tutorials are marked in green.

week date sections material covered homework and other notes
1 2/8 1.1-1.2 Basic set theory Chap. 1: 1, 3, 4, 5, 6
2 5/8 1.3-1.4 Probabilities Chap. 1: 8, 11, 12, 13, 15, 19, 21
7/8 1.5-1.6 Independence Chap. 1: 36, 37, 40, 43, 45, 47
8/8 -

Quiz 1

-
9/8 -

Holiday

3 12/8 -

Holiday

14/8 2.1-2.2 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 Joint random variables Chap. 2: 49, 50, 53, 55
5 26/8 2.5 Independence and covariance
28/8 2.6 Moment generating functions
29/8 -

Quiz 3

-
30/8 2.6 Moment generating functions
6 2/9 -

Holiday

4/9 2.8 Limit theorems
5/9 -

Quiz 4

-
6/9 2.9 Stochastic processes
7 9/9 3.1-3.3 Conditional probability
11/9 3.4 Expectations by conditioning
12/9 -

Quiz 5

-
13/9 3.4 Conditional Variance formula
8 16/9 3.5 Probabilities by conditioning
18/9 3.6 A random graph model
19/9 -

Quiz 6

-
20/9 4.1-4.2 Introduction to Markov chains
9 23/9

No class (midterm week)

25/9 Midsemester exam
26/9 -

No class (midterm week)

-
27/9

No class (midterm week)

10 30/9 4.2 Restrictions of Markov chains
2/10 -

Holiday

3/10 -

Quiz 7

-
4/10 4.3 Classification of states
11 7/10 4.4 Long run proportions
9/10 4.4 Stationary distribution
10/10 -

Quiz 8

-
11/10 4.6 Examples of Markov chains
12 14/10
16/10
17/10 -

Quiz 9

-
18/10
13 21/10
23/10
24/10 -

Quiz 10

-
25/10
14 28/10
30/10
31/10 -

Quiz 11

-
1/11 -

Holiday

15 4/11
6/11
7/11 -

Quiz 12

-
8/11
16 11/11
13/11
14/11 -

Quiz 13

-
15/11
16 18/11
20/11
21/11 -

Quiz 14

-
22/11