All the lecture notes are available from the class notes page. 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.

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

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,
After midsem:
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.

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