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### Manjunath Krishnapur

Department of Mathematics, Indian Institute of Science, Bangalore 560 012

### Probability models (Aug-Dec 2017)

Mon, Wed, Fri 5:00-6:00, LH-1, Mathematics department

Tutorials by Lakshmi Priya: Thu 5:30-6:30, LH-1, Mathematics department. Quizzes will be in tutorials.

Description: This is the first course in probability theory. Probability is an intuitive concept, and we often use the words such as probably, by chance, luckily, an unbelievable coincidence etc., which indicate uncertainty. Yet, probability theory is a part of mathematics. The aim in this course is to learn the basic concepts of this mathematical theory of probability, as well as develop an intuitive understanding of what these concepts mean and how they are applied in "real life situations". In this course we will stick to discrete probability spaces, where the mathematical sophistication needed is little. A natural continuation is the Probability theory course offered in the next semester, where you will learn the measure theoretical foundations of probability.

Grading: The final grade will be based on regular quizzes (25%), two class tests (25% together) and the final exam (50%). Solving problems (preferably many more than given in the problem sets) is absolutely crucial to develop an understanding of the subject.

Texts and other resources: Sheldon Ross' Introduction to probability models is the primary text for the course. We will try to cover most of chapters 1-6 and chapter 11, although I will not strictly follow the book at all times. Another excellent book is William Feller's classic treatise An introduction to probability theory and its applications - vol. 1. Both these book have lots of examples and problems (and available at Tata book house). In addition to books, there are various resources on the web (for example) regarding basic probability. The book by Grimmett and Stirzaker titled Probability and random processes is very good, but starts with the language of sigma algebras which we do not introduce in this course.
Lecture notes The first part roughly coincides with the first half of this course. The second half of the course will be on Markov chains.