MTL 601 (Probability and Statistics)

4 Credits (3-1-0) 

Lectures: Tue, Thu and Fri 11.00 - 11.50 AM at MZ 194.

Major Marks


Axiomatic definition of a probability measure, examples, properties of the probability measure, finite probability space, conditional probability and Baye's formula, countable probability space, general probability space


Random variables, examples, sigma-field generated by a random variable, tail sigma-field, probability space on R induced by a random variable


Distribution - definition and examples, properties, characterization, Jordan decomposition theorem, discrete, continuous and mixed random variables, standard discrete and continuous distributions


Two dimension random variables, joint distributions, marginal distributions, operations on random variables and their corresponding distributions, multidimensional random variables and their distributions


Expectation of a random variable, expectation of a discrete and a continuous random variable, moments and moment generating function, correlation, covariance and regression


Various modes of convergence, convergence in distribution, weak convergence of generalized distributions, Helly-Bray theorems, Scheffe's theorem


Characteristic function definition and examples, properties, conjugate distributions, uniqueness and inversion theorems, moments using characteristic function, Paul Levy's continuity property of characteristic functions


Independent events, sigma-fields and random variables, characterization of independent random variables, Borel 0-1 criteria, Kolmogorov 0-1 criteria


Weak law of large numbers, strong law of large numbers, central limit theorem Liapunov's and Lindberg's condition, Lindeberg-Levy form


Sampling distributions, characteristics, asymptotic properties


Theory of estimation Classification of estimates, methods of estimates, confidence regions, MVUE, Cramer Rao Theorem, Rao Blackwellization


Tests of significance General theory of testing hypothesis, choice of a test, simple and composite hypothesis, tests of simple and composite hypothesis


Goodness of fit test, Chi-square test, Kolmogorov Smirnov test, analysis of variance


Main Text Books


1.    An Introduction to Probability and Statistics, Vijay K. Rohatgi and A.K. Md. Ehsanes Saleh, John Wiley, second edition, 2001.

2.    Introductory Probability and Statistical Applications, Paul L. Mayer, Addison-Wesley, Second Edition, 1970.

3.    Statistical Inference, George Casella and Roger L. Beger Saleh, Duxbury Press, second edition, 2001.

4.    Introduction to Probability and Stochastic Processes with Applications, Liliana Blanco Castaneda, Viswanathan Arunachalam, Selvamuthu Dharmaraja, Wiley, Asian Edition, Jan. 2016.

Tutorial Sheets

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 Answer

Tutorial Sheet 2 Answer

Tutorial Sheet 3 Answer

Tutorial Sheet 4 Answer

Tutorial Sheet 5 Answer

Tutorial Sheet 6 Answer

Scheme of Evaluation


Two Minor Tests of 25 Marks each

2 X 25


One Major Examination

1 X 50







         Students are encouraged to contact the Course Coordinator or Tutorial Teachers for any difficulties regarding the course.

         Only those students who could not appear for one of the minor tests due to medical reasons are eligible for the make up examination which will be conducted before the major examination. However, submission of a valid medical certificate adhering to the institute norms is mandatory.

         The evaluated minor answer books will be returned to the students and they must retain with them as a proof of the marks secured.

INFORMATION about the Instructors



Room No.

Phone No.


S Dharmaraja

MZ 164


This page maintained by Dr. S. Dharmaraja and last updated Monday, Nov. 27, 2017.