This is the class webpage for Probability Theory I
(2025).
Teacher: Arnab Chakraborty
Email:arnabc74 at gmail
Office: Applied Statistics Unit (ASU) Room 914 (S N Bose Bhavan 9th floor)
Office hour (time slot for students to meet me in my office): Friday 5pm to 6pm. Sorry, but you
are not encouraged to visit my office at other times, as I happen to be a busy person.
Notice
board
Whenever I update anything in the class webpage, I shall mention it in the notice board.
These notes are the
definitive source of material for this course. The practice
problems given in the notes are indicative of the problems you
are likely to face in the exams.
We shall not follow any single textbook. All the material that we
shall cover may be found in the following
books.
A First Course in Probability Theory by Sheldon
Ross: The book is easy to
read. We shall cover only about half the book in this
semester. Cheap Indian edition available.
Introduction to Probability Theory by Hoel, Port and Stone: Another nice book.
Thin. May not be available offline (except in our library).
Probability Theory (Vol 1) by William Feller:
A classic book which (in my opinion) is not very
well-organised. But it contains lots of discussions on practical
applications of probability. We shall pick some advanced topics
from this book from time to time. Cheap Indian edition
available. Most students buy one copy of this book, and then
never read it.
Counterexamples in Probability by Jordan M
Stoyanov: Lots of fun examples to baffle (and improve) your
intuition. We shall borrow some of these examples.
Fifty challenging problem in probability with
solutions by Frederick Mosteller
A Course in Applied Stochastic Processes by A Goswami and B V Rao: We shall
borrow only the discussion of branching processes from this book.
Up to midsem: Elementary concepts: experiments, outcomes, sample space,
events.
Discrete sample spaces and probability models.
Equally likely set-up and combinatorial probability.
Fluctuations in coin tossing and random walks,
Combination of events.
Composite experiments, conditional probability, Polya's urn scheme, Bayes theorem,
independence.
Discrete random
variables.
Expectation/mean,
functions of discrete random
variables,
Variance, moments,
moment generating functions
probability generating functions.
Standard discrete distributions.
Joint distributions of discrete random
variables,
independence,
conditional distributions, conditional expectation.
Distribution of sum of two independent random
variables. Functions of more than one discrete random
variables.