DEPARTMENT OF MATHEMATICS

MAL 509 (Probability Theory) 4 Credits (

INFORMATION SHEET

Probability as a set function, Borel-field and extension of probability measure. Random variables as Borel measurable functions. Distribution
function. Multi-dimensional random variables. Conditional probability and statistical independence. Moments, correlation and regression. Characteristic
function, uniqueness and inversion theorems. Convergence
of sequence of random variables and various modes of convergence. Laws of large numbers. Central limit
theorem, Liapunov’s and Lindeberg-Feller’s
theorem, Law of iterated logarithms.

REFERENCE BOOKS

- Main Text Book:
*An Introduction to Probability and Statistics*, Vijay K. Rohatgi and A.K. Md. Ehsanes Saleh, John Wiley, second edition, 2001. *Introduction to Probability and Stochastic Processes with Applications, Liliana Blanco Castaneda, Viswanathan Arunachalam, Selvamuthu Dharmaraja, Wiley, New Jersey, June 2012.**Modern Probability Theory*, B.R. Bhat, New Age Publishers, third edition, 1981.*An Introduction to Probability Theory and its Applications, Vol. I & II,*William Feller, John Wiley, second edition, 2000.

Note: It seems, some students found that the answers provided for few problems in the following tutorial sheets are not correct. Please let me know these errors by email.

Tutorial Sheet 1

See Course Website: http://web.iitd.ac.in/~dharmar/mal509/main.html
for further details.

(S. Dharmaraja)

COURSE INSTRUCTOR