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

INFORMATION SHEET

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

50

One Major Examination

1 X 50

50

 

Total

100

 

IMPORTANT INFORMATION

         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

 

Name

Room No.

Phone No.

Email

S Dharmaraja

MZ 164

7104

dharmar@maths.iitd.ac.in

This page maintained by Dr. S. Dharmaraja mailto:dharmar@maths.iitd.ac.in and last updated Monday, Nov. 27, 2017.